Journal of Graph Theory最新文献
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Automorphism Group of a Wreath Product of Binary Structures
二元结构环积的自同构群
IF 1
3区 数学
Geňa Hahn, Pierre Ille
{"title":"Automorphism Group of a Wreath Product of Binary Structures","authors":"Geňa Hahn, Pierre Ille","doi":"10.1002/jgt.70071","DOIUrl":"https://doi.org/10.1002/jgt.70071","url":null,"abstract":"<div>\u0000 \u0000 <p>We consider the question of when the automorphism group of the wreath (lexicographic) product of two structures is the wreath product of the automorphism groups of the two structures. Sabidussi gave partial soluLet us formalize our presentationtions, others (Hemminger, Hahn, Dobson and Morris) continued the work. All the previous work ignored one particular case and here we complete the study by generalizing to binary structures using modular decomposition.</p></div>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 3","pages":"428-447"},"PeriodicalIF":1.0,"publicationDate":"2026-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148904027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weak Degeneracy of Planar Graphs
平面图的弱简并
IF 1
3区 数学
Anton Bernshteyn, Eugene Lee, Evelyne Smith-Roberge
{"title":"Weak Degeneracy of Planar Graphs","authors":"Anton Bernshteyn, Eugene Lee, Evelyne Smith-Roberge","doi":"10.1002/jgt.70070","DOIUrl":"https://doi.org/10.1002/jgt.70070","url":null,"abstract":"<p>The weak degeneracy of a graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 </semantics></math> is a numerical parameter that was recently introduced by the first two authors with the aim of understanding the power of greedy algorithms for graph coloring. Every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-degenerate graph is weakly <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-degenerate, but the converse is not true in general (e.g., all connected <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-regular graphs except cycles and cliques are weakly <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>d</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </semantics></math>-degenerate). If <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 </semantics></math> is weakly <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>d</mi>\u0000 </mrow>\u0000 </semantics></math>-degenerate, then the list-chromatic number of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 </semantics></math> is at most <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>d</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 </semantics></math>, and the same upper bound holds for various other parameters such as the DP-chromatic number and the paint number. Here we rectify a mistake in a paper of the first two authors and give a correct proof that planar graphs are weakly 4-degenerate, strengthening the famous result of Thomassen that planar graphs are 5-list-colorable.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 3","pages":"399-410"},"PeriodicalIF":1.0,"publicationDate":"2026-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70070","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148904396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hitting Times in the Binomial Random Graph
二项随机图中的命中次数
IF 1
3区 数学
Bertille Granet, Felix Joos, Jonathan Schrodt
{"title":"Hitting Times in the Binomial Random Graph","authors":"Bertille Granet, Felix Joos, Jonathan Schrodt","doi":"10.1002/jgt.70057","DOIUrl":"https://doi.org/10.1002/jgt.70057","url":null,"abstract":"<p>Fix <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70057:jgt70057-math-0001\" wiley:location=\"equation/jgt70057-math-0001.png\"><mrow><mrow><mi>k</mi><mo>unicode{x02265}</mo><mn>2</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>, choose <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mfrac>\u0000 <mrow>\u0000 <mi>log</mi>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 \u0000 <msup>\u0000 <mi>n</mi>\u0000 \u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>∕</mo>\u0000 \u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mfrac>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mi>p</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>1</mn>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>Ω</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mfrac>\u0000 <mrow>\u0000 <msup>\u0000 <mi>log</mi>\u0000 \u0000 <mn>4</mn>\u0000 </msup>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"377-393"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70057","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Clique-Building Game of Erdős
在一个集团建设游戏Erdős
IF 1
3区 数学
Alexandru Malekshahian, Sam Spiro
{"title":"On a Clique-Building Game of Erdős","authors":"Alexandru Malekshahian, Sam Spiro","doi":"10.1002/jgt.70061","DOIUrl":"https://doi.org/10.1002/jgt.70061","url":null,"abstract":"<p>The following game was introduced in a list of open problems from 1983 attributed to Erdős: two players take turns claiming edges of a <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70061:jgt70061-math-0001\" wiley:location=\"equation/jgt70061-math-0001.png\"><mrow><mrow><msub><mi>K</mi><mi>n</mi></msub></mrow></mrow></math></annotation>\u0000 </semantics></math> until all edges are exhausted. Player 1 wins the game if the largest clique that they claim at the end is strictly larger than the largest clique of their opponent; otherwise, Player 2 wins the game. Erdős conjectured that Player 2 always wins this game for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>3</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70061:jgt70061-math-0002\" wiley:location=\"equation/jgt70061-math-0002.png\"><mrow><mrow><mi>n</mi><mo>unicode{x02265}</mo><mn>3</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>. We make the first known progress on this problem, proving that this holds for at least 3/4 of all such <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70061:jgt70061-math-0003\" wiley:location=\"equation/jgt70061-math-0003.png\"><mrow><mrow><mi>n</mi></mrow></mrow></math></annotation>\u0000 </semantics></math>. We also address a biased version of this game, as well as the corresponding degree-building game, both of which were originally proposed by Erdős as well.</p>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"208-221"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70061","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lower Bounds for Maximum Weight Bisections of Weighted Triangle-Free Subcubic Graphs
加权无三角次三次图的最大权等分下界
IF 1
3区 数学
Stefanie Gerke, Gregory Gutin, Anders Yeo, Yacong Zhou
{"title":"Lower Bounds for Maximum Weight Bisections of Weighted Triangle-Free Subcubic Graphs","authors":"Stefanie Gerke, Gregory Gutin, Anders Yeo, Yacong Zhou","doi":"10.1002/jgt.70056","DOIUrl":"https://doi.org/10.1002/jgt.70056","url":null,"abstract":"<p>A bisection of a graph is a cut in which the number of vertices in the two parts of the cut differ by at most 1. In this paper, we consider maximum weight bisections of edge-weighted triangle-free subcubic graphs and show that every weighted triangle-free subcubic graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>w</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70056:jgt70056-math-0001\" wiley:location=\"equation/jgt70056-math-0001.png\"><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mrow><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>w</mi></mrow><mo>)</mo></mrow></mrow></math></annotation>\u0000 </semantics></math> has a bisection with weight at least <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>θ</mi>\u0000 \u0000 <mo>⋅</mo>\u0000 \u0000 <mi>w</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70056:jgt70056-math-0002\" wiley:location=\"equation/jgt70056-math-0002.png\"><mrow><mi>unicode{x003B8}</mi><mo>unicode{x022C5}</mo><mi>w</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></annotation>\u0000 </semantics></math> unless <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>≅</mo>\u0000 \u0000 <msub>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <mn>1</mn>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"252-273"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70056","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Coarse Geometric Approach to Graph Layout Problems
图布局问题的粗糙几何方法
IF 1
3区 数学
Wanying Huang, David Hume, Samuel J. Kelly, Ryan Lam
{"title":"A Coarse Geometric Approach to Graph Layout Problems","authors":"Wanying Huang, David Hume, Samuel J. Kelly, Ryan Lam","doi":"10.1002/jgt.70058","DOIUrl":"https://doi.org/10.1002/jgt.70058","url":null,"abstract":"<p>We define a range of new coarse geometric invariants based on various graph–theoretic measures of complexity for finite graphs, including treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these invariants can be used to define functions which satisfy a strong monotonicity property, namely, they are monotonically nondecreasing with respect to a large-scale geometric generalisation of graph inclusion, and as such have potential applications in coarse geometry and geometric group theory. On the graph–theoretic side, we prove asymptotically optimal bounds on most of the above widths for the family of all finite subgraphs of any bounded degree graph whose separation profile is known to be of the form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msup>\u0000 <mi>r</mi>\u0000 \u0000 <mi>a</mi>\u0000 </msup>\u0000 \u0000 <mi>log</mi>\u0000 \u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>r</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mi>b</mi>\u0000 </msup>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math display=\"inline\" altimg=\"urn:x-wiley:03649024:media:jgt70058:jgt70058-math-0001\" xmlns=\"http://www.w3.org/1998/Math/MathML\" wiley:location=\"equation/jgt70058-math-0001.png\"><mrow><mrow><msup><mi>r</mi><mi>a</mi></msup><mi>log</mi><msup><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mi>b</mi></msup></mrow></mrow></math></annotation>\u0000 </semantics></math> for some <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>a</mi>\u0000 \u0000 <mo>></mo>\u0000 \u0000 <mn>0</mn>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math display=\"inline\" altimg=\"urn:x-wiley:03649024:media:jgt70058:jgt70058-math-0002\" xmlns=\"http://www.w3.org/1998/Math/MathML\" wiley:location=\"equation/jgt70058-math-0002.png\"><mrow><mrow><mi>a</mi><mo>unicode{x0003E}</mo><mn>0</mn></mrow></mrow></math></annotation>\u0000 </semantics></math>. This large class includes Diestel–Leader graphs, all Cayley graphs of nonvirtually cyclic polycyclic groups, uniform lattices in","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"169-194"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.70058","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Deep-Commuting Graph of Groups
关于群的深度可交换图
IF 1
3区 数学
Bahram Arvin, Behrouz Edalatzadeh, Ali Reza Salemkar
{"title":"On Deep-Commuting Graph of Groups","authors":"Bahram Arvin, Behrouz Edalatzadeh, Ali Reza Salemkar","doi":"10.1002/jgt.70059","DOIUrl":"https://doi.org/10.1002/jgt.70059","url":null,"abstract":"<div>\u0000 \u0000 <p>The deep-commuting graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mtext>DCom</mtext>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0001\" wiley:location=\"equation/jgt70059-math-0001.png\"><mrow><mrow><mtext>DCom</mtext><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> of a finite group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0002\" wiley:location=\"equation/jgt70059-math-0002.png\"><mrow><mrow><mi>G</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> is the graph with vertex set <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0003\" wiley:location=\"equation/jgt70059-math-0003.png\"><mrow><mrow><mi>G</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> such that two vertices <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0004\" wiley:location=\"equation/jgt70059-math-0004.png\"><mrow><mrow><mi>x</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>y</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70059:jgt70059-math-0005\" wiley:location=\"equation/jgt70059-math-0005.png\"><mrow><mrow><mi>y</mi></mrow></mrow>","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"195-207"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bipartite Graphs With Minimum Degree at Least 15 Are Antimagic
最小度至少为15的二部图是反幻的
IF 1
3区 数学
Kecai Deng
{"title":"Bipartite Graphs With Minimum Degree at Least 15 Are Antimagic","authors":"Kecai Deng","doi":"10.1002/jgt.70069","DOIUrl":"https://doi.org/10.1002/jgt.70069","url":null,"abstract":"<div>\u0000 \u0000 <p>An antimagic labeling of a graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>V</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>E</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70069:jgt70069-math-0001\" wiley:location=\"equation/jgt70069-math-0001.png\"><mrow><mrow><mi>G</mi><mo>=</mo><mrow><mo>(</mo><mrow><mi>V</mi><mo>,</mo><mi>E</mi></mrow><mo>)</mo></mrow></mrow></mrow></math></annotation>\u0000 </semantics></math> is a one-to-one mapping <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>f</mi>\u0000 \u0000 <mo>:</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mo>→</mo>\u0000 \u0000 <mrow>\u0000 <mo>{</mo>\u0000 \u0000 <mrow>\u0000 <mn>1</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mo>…</mo>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mo>∣</mo>\u0000 \u0000 <mi>E</mi>\u0000 \u0000 <mo>∣</mo>\u0000 </mrow>\u0000 \u0000 <mo>}</mo>\u0000 </mrow>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70069:jgt70069-math-0002\" wiley:location=\"equation/jgt70069-math-0002.png\"><mrow><mrow><mi>f</mi><mo>:</mo><mi>E</mi><mo>unicode{x02192}</mo><mrow><mo class=\"MathClass-open\">{</mo><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>unicode{x02026}</mo><mo>,</mo><mo>u","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"348-376"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The k -Radius of 2-Connected Graphs
2连通图的k k半径
IF 1
3区 数学
Peter Dankelmann, Paul Horn
{"title":"The \u0000 \u0000 \u0000 k\u0000 \u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0001\" wiley:location=\"equation/jgt70065-math-0001.png\"><mrow><mi>k</mi></mrow></math>\u0000 -Radius of 2-Connected Graphs","authors":"Peter Dankelmann, Paul Horn","doi":"10.1002/jgt.70065","DOIUrl":"https://doi.org/10.1002/jgt.70065","url":null,"abstract":"<div>\u0000 \u0000 <p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0002\" wiley:location=\"equation/jgt70065-math-0002.png\"><mrow><mi>G</mi></mrow></math></annotation>\u0000 </semantics></math> be a connected graph. If <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0003\" wiley:location=\"equation/jgt70065-math-0003.png\"><mrow><mi>S</mi></mrow></math></annotation>\u0000 </semantics></math> is a set of vertices of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0004\" wiley:location=\"equation/jgt70065-math-0004.png\"><mrow><mi>G</mi></mrow></math></annotation>\u0000 </semantics></math>, and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>v</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0005\" wiley:location=\"equation/jgt70065-math-0005.png\"><mrow><mi>v</mi></mrow></math></annotation>\u0000 </semantics></math> is a vertex of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0006\" wiley:location=\"equation/jgt70065-math-0006.png\"><mrow><mi>G</mi></mrow></math></annotation>\u0000 </semantics></math>, then the distance <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mi>d</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>S</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70065:jgt70065-math-0007\" wiley:location","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"286-310"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Realizing Degree Sequences With S 3 -Connected Graphs
用S3连通图实现度序列
IF 1
3区 数学
Rui Guan, Chenglin Jiang, Hong-Jian Lai, Jiaao Li, Xinyuan Li
{"title":"Realizing Degree Sequences With \u0000 \u0000 \u0000 \u0000 \u0000 S\u0000 3\u0000 \u0000 \u0000 \u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70062:jgt70062-math-0001\" wiley:location=\"equation/jgt70062-math-0001.png\"><mrow><mrow><msub><mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">S</mi><mn>3</mn></msub></mrow></mrow></math>\u0000 -Connected Graphs","authors":"Rui Guan, Chenglin Jiang, Hong-Jian Lai, Jiaao Li, Xinyuan Li","doi":"10.1002/jgt.70062","DOIUrl":"https://doi.org/10.1002/jgt.70062","url":null,"abstract":"<div>\u0000 \u0000 <p>A graph <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70062:jgt70062-math-0002\" wiley:location=\"equation/jgt70062-math-0002.png\"><mrow><mrow><mi>G</mi></mrow></mrow></math></annotation>\u0000 </semantics></math> is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>S</mi>\u0000 \u0000 <mn>3</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70062:jgt70062-math-0003\" wiley:location=\"equation/jgt70062-math-0003.png\"><mrow><mrow><msub><mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">S</mi><mn>3</mn></msub></mrow></mrow></math></annotation>\u0000 </semantics></math>-connected if, for any mapping <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <mi>β</mi>\u0000 \u0000 <mo>:</mo>\u0000 \u0000 <mi>V</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>↦</mo>\u0000 \u0000 <msub>\u0000 <mi>Z</mi>\u0000 \u0000 <mn>3</mn>\u0000 </msub>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> <math xmlns=\"http://www.w3.org/1998/Math/MathML\" altimg=\"urn:x-wiley:03649024:media:jgt70062:jgt70062-math-0004\" wiley:location=\"equation/jgt70062-math-0004.png\"><mrow><mrow><mi>unicode{x003B2}</mi><mo>:</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>unicode{x021A6}</mo><msub><mi mathvariant=\"double-struck\">Z</mi><mn>3</mn></msub></mrow></mrow></math></annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mo>∑</mo>\u0000 \u0000 <mrow>\u0000 <mi>v</mi>\u0000 \u0000 ","PeriodicalId":16014,"journal":{"name":"Journal of Graph Theory","volume":"113 2","pages":"222-236"},"PeriodicalIF":1.0,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148704254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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