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Theory and Applications of Graphs最新文献

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On the uniqueness of continuation of a partially defined metric 部分定义度规延拓的唯一性
Theory and Applications of Graphs Pub Date : 2022-01-01 DOI: 10.20429/tag.2022.100101
E. Petrov
{"title":"On the uniqueness of continuation of a partially defined metric","authors":"E. Petrov","doi":"10.20429/tag.2022.100101","DOIUrl":"https://doi.org/10.20429/tag.2022.100101","url":null,"abstract":"","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67545449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Path-Stick Solitaire on Graphs 图上的路径棒纸牌
Theory and Applications of Graphs Pub Date : 2022-01-01 DOI: 10.20429/tag.2022.090212
Jan-Hendrik de Wiljes, M. Kreh
{"title":"Path-Stick Solitaire on Graphs","authors":"Jan-Hendrik de Wiljes, M. Kreh","doi":"10.20429/tag.2022.090212","DOIUrl":"https://doi.org/10.20429/tag.2022.090212","url":null,"abstract":"","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67545880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
One-factorizations of the complete graph $K_{p+1}$ arising from parabolas 由抛物线引起的完全图$K_{p+1}$的一分解
Theory and Applications of Graphs Pub Date : 2022-01-01 DOI: 10.20429/tag.2022.090202
G. Kiss, Nicola Pace, A. Sonnino
{"title":"One-factorizations of the complete graph $K_{p+1}$ arising from parabolas","authors":"G. Kiss, Nicola Pace, A. Sonnino","doi":"10.20429/tag.2022.090202","DOIUrl":"https://doi.org/10.20429/tag.2022.090202","url":null,"abstract":"There are three types of affine regular polygons in AG(2, q): ellipse, hyperbola and parabola. The first two cases have been investigated in previous papers. In this note, a particular class of geometric one-factorizations of the complete graph Kn arising from parabolas is constructed and described in full detail. With the support of computer aided investigation, it is also conjectured that up to isomorphisms this is the only one-factorization where each one-factor is either represented by a line or a parabola.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67545865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Even 2-Factor in the Line Graph of a Cubic Graph 三次图的线形图中的一个偶2因子
Theory and Applications of Graphs Pub Date : 2022-01-01 DOI: 10.20429/tag.2022.090107
Seungjae Eom, K. Ozeki
{"title":"An Even 2-Factor in the Line Graph of a Cubic Graph","authors":"Seungjae Eom, K. Ozeki","doi":"10.20429/tag.2022.090107","DOIUrl":"https://doi.org/10.20429/tag.2022.090107","url":null,"abstract":". An even 2-factor is one such that each cycle is of even length. A 4-regular graph G is 4-edge-colorable if and only if G has two edge-disjoint even 2-factors whose union contains all edges in G . It is known that the line graph of a cubic graph without 3-edge-coloring is not 4-edge-colorable. Hence, we are interested in whether those graphs have an even 2-factor. Bonisoli and Bonvicini proved that the line graph of a connected cubic graph G with an even number of edges has an even 2-factor, if G has a perfect matching [Even cycles and even 2-factors in the line graph of a simple graph, The Electron. J. Combin. 24 (2017), P4.15]. In this paper, we extend this theorem to the line graph of a connected cubic graph G satisfying certain conditions.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67545778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterization of outerplanar graphs with equal 2-domination and domination numbers 具有相等2-支配数和支配数的外平面图的表征
Theory and Applications of Graphs Pub Date : 2022-01-01 DOI: 10.20429/tag.2022.090201
Naoki Matsumoto
{"title":"Characterization of outerplanar graphs with equal 2-domination and domination numbers","authors":"Naoki Matsumoto","doi":"10.20429/tag.2022.090201","DOIUrl":"https://doi.org/10.20429/tag.2022.090201","url":null,"abstract":"A k -domination number of a graph G is minimum cardinality of a k -dominating set of G , where a subset S ⊆ V ( G ) is a k -dominating set if each vertex v ∈ V ( G ) S is adjacent to at least k vertices in S . It is known that for any graph G with ∆( G ) ≥ k ≥ 2, γ k ( G ) ≥ γ ( G ) + k − 2, and then γ k ( G ) > γ ( G ) for any k ≥ 3, where γ ( G ) = γ 1 ( G ) is the usual domination number. Thus, it is the most interesting problem to characterize graphs G with γ 2 ( G ) = γ ( G ). In this paper, we characterize outerplanar graphs with equal 2-domination and domination numbers.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67545819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
HS-integral and Eisenstein integral mixed circulant graphs HS积分与Eisenstein积分混合循环图
Theory and Applications of Graphs Pub Date : 2021-12-15 DOI: 10.20429/tag.2023.100103
Monu Kadyan, B. Bhattacharjya
{"title":"HS-integral and Eisenstein integral mixed circulant graphs","authors":"Monu Kadyan, B. Bhattacharjya","doi":"10.20429/tag.2023.100103","DOIUrl":"https://doi.org/10.20429/tag.2023.100103","url":null,"abstract":"A mixed graph is called second kind hermitian integral ( HS-integral ) if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers. A mixed graph is called Eisenstein integral if the eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. We characterize the set S for which a mixed circulant graph Circ( Z n , S ) is HS-integral. We also show that a mixed circulant graph is Eisenstein integral if and only if it is HS-integral. Further, we express the eigenvalues and the HS-eigenvalues of unitary oriented circulant graphs in terms of generalized M¨obius function.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45646115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Optimal orientations of Vertex-multiplications of Trees with Diameter 4 直径为4的树的顶点乘法的最优方向
Theory and Applications of Graphs Pub Date : 2021-10-18 DOI: 10.20429/tag.2023.10106
W. Wong, E. G. Tay
{"title":"Optimal orientations of Vertex-multiplications of Trees with Diameter 4","authors":"W. Wong, E. G. Tay","doi":"10.20429/tag.2023.10106","DOIUrl":"https://doi.org/10.20429/tag.2023.10106","url":null,"abstract":"Koh and Tay proved a fundamental classification of $G$ vertex-multiplications into three classes $mathscr{C}_0, mathscr{C}_1$ and $mathscr{C}_2$. They also showed that any vertex-multiplication of a tree with diameter at least 3 does not belong to the class $mathscr{C}_2$. Of interest, $G$ vertex-multiplications are extensions of complete $n$-partite graphs and Gutin characterised complete bipartite graphs with an ingenious use of Sperner's Theorem. In this paper, we investigate vertex-multiplications of trees with diameter $4$ in $mathscr{C}_0$ (or $mathscr{C}_1$) and exhibit its intricate connections with problems in Sperner Theory, thereby extending Gutin's approach. Let $s$ denote the vertex-multiplication of the central vertex. We almost completely characterise the case of even $s$ and give a complete characterisation for the case of odd $sge 3$.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44577503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On Graphs with Proper Connection Number 2 关于具有适当连接数2的图
Theory and Applications of Graphs Pub Date : 2021-08-02 DOI: 10.20429/tag.2021.080202
J. Faudree, Leah Wrenn Berman, G. G. Chappell, C. Hartman, J. Gimbel, G. Williams
{"title":"On Graphs with Proper Connection Number 2","authors":"J. Faudree, Leah Wrenn Berman, G. G. Chappell, C. Hartman, J. Gimbel, G. Williams","doi":"10.20429/tag.2021.080202","DOIUrl":"https://doi.org/10.20429/tag.2021.080202","url":null,"abstract":"An edge-colored graph is properly connected if for every pair of vertices u and v there exists a properly colored uv-path (i.e. a uv-path in which no two consecutive edges have the same color). The proper connection number of a connected graph G, denoted pc(G), is the smallest number of colors needed to color the edges of G such that the resulting colored graph is properly connected. An edge-colored graph is flexibly connected if for every pair of vertices u and v there exist two properly colored paths between them, say P and Q, such that the first edges of P and Q have different colors and the last edges of P and Q have different colors. The flexible connection number of a connected graph G, denoted fpc(G), is the smallest number of colors needed to color the edges of G such that the resulting colored graph is flexibly connected. In this paper, we demonstrate several methods for constructing graphs with pc(G) = 2 and fpc(G) = 2. We describe several families of graphs such that pc(G) ≥ 2 and we settle a conjecture from [3]. We prove that if G is connected and bipartite, then pc(G) = 2 is equivalent to being 2-edge-connected and fpc(G) = 2 is equivalent to the existence of a path through all cut-edges. Finally, it is proved that every connected, k-regular, Class 1 graph has flexible connection number 2.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47373895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Color Number of Cubic Graphs Having a Spanning Tree with a Bounded Number of Leaves 具有有界叶数生成树的三次图的色数
Theory and Applications of Graphs Pub Date : 2021-07-31 DOI: 10.20429/tag.2021.080201
Analen Malnegro, Gina A. Malacas, K. Ozeki
{"title":"The Color Number of Cubic Graphs Having a Spanning Tree with a Bounded Number of Leaves","authors":"Analen Malnegro, Gina A. Malacas, K. Ozeki","doi":"10.20429/tag.2021.080201","DOIUrl":"https://doi.org/10.20429/tag.2021.080201","url":null,"abstract":"The color number c(G) of a cubic graph G is the minimum cardinality of a color class of a proper 4-edge-coloring of G. It is well-known that every cubic graph G satisfies c(G) = 0 if G has a Hamiltonian cycle, and c(G) ≤ 2 if G has a Hamiltonian path. In this paper, we extend these observations by obtaining a bound for the color number of cubic graphs having a spanning tree with a bounded number of leaves.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49307673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Rainbow Cycles and Proper Edge Colorings of Generalized Polygons 关于广义多边形的彩虹环与真边着色
Theory and Applications of Graphs Pub Date : 2021-06-09 DOI: 10.20429/tag.2022.100102
Matt Noble
{"title":"On Rainbow Cycles and Proper Edge Colorings of Generalized Polygons","authors":"Matt Noble","doi":"10.20429/tag.2022.100102","DOIUrl":"https://doi.org/10.20429/tag.2022.100102","url":null,"abstract":"An edge coloring of a simple graph $G$ is said to be textit{proper rainbow-cycle-forbidding} (PRCF, for short) if no two incident edges receive the same color and for any cycle in $G$, at least two edges of that cycle receive the same color. A graph $G$ is defined to be textit{PRCF-good} if it admits a PRCF edge coloring, and $G$ is deemed textit{PRCF-bad} otherwise. In recent work, Hoffman, et al. study PRCF edge colorings and find many examples of PRCF-bad graphs having girth less than or equal to 4. They then ask whether such graphs exist having girth greater than 4. In our work, we give a straightforward counting argument showing that the Hoffman-Singleton graph answers this question in the affirmative for the case of girth 5. It is then shown that certain generalized polygons, constructed of sufficiently large order, are also PRCF-bad, thus proving the existence of PRCF-bad graphs of girth 6, 8, 12, and 16.","PeriodicalId":37096,"journal":{"name":"Theory and Applications of Graphs","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47145326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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