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Electronic Journal of Graph Theory and Applications最新文献

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Multiplicity-free gonality on graphs 图上的无多重性
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.2
Frances Dean, Max Everett, Ralph Morrison
{"title":"Multiplicity-free gonality on graphs","authors":"Frances Dean, Max Everett, Ralph Morrison","doi":"10.5614/ejgta.2023.11.2.2","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.2","url":null,"abstract":"The divisorial gonality of a graph is the minimum degree of a positive rank divisor on that graph. We introduce the multiplicity-free gonality of a graph, which restricts our consideration to divisors that place at most 1 chip on each vertex. We give a sufficient condition in terms of vertex-connectivity for these two versions of gonality to be equal; and we show that no function of gonality can bound multiplicity-free gonality, even for simple graphs. We also prove that multiplicity-free gonality is NP-hard to compute, while still determining it for graph families for which gonality is currently unknown. We also present new gonalities, such as for the wheel graphs.","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135321968","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 z-cycle factorizations with two associate classes where z is 2a and a is even 关于两个相关类的z环分解，其中z是2a, a是偶数
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.9
Joshua Lambert, Michael Tiemeyer
{"title":"On z-cycle factorizations with two associate classes where z is 2a and a is even","authors":"Joshua Lambert, Michael Tiemeyer","doi":"10.5614/ejgta.2023.11.2.9","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.9","url":null,"abstract":"Let K = K ( a , p ; λ 1 , λ 2 ) be the multigraph with: the number of parts equal to p ; the number of vertices in each part equal to a ; the number of edges joining any two vertices of the same part equal to λ 1 ; and the number of edges joining any two vertices of different parts equal to λ 2 . The existence of C 4 -factorizations of K has been settled when a is even; when a ≡ 1 (mod 4) with one exception; and for very few cases when a ≡ 3 (mod 4) . The existence of C z -factorizations of K has been settled when a ≡ 1 (mod z ) and λ 1 is even, and when a ≡ 0 (mod z ) . In this paper, we give a construction for C z -factorizations of K for z = 2 a when a is even.","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"36 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135321970","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
Graceful labeling construction for some special tree graph using adjacency matrix 利用邻接矩阵构造一些特殊树形图的优美标注
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.1
Nikson Simarmata, Ikhlas Pratama Sandy, Kiki A. Sugeng
{"title":"Graceful labeling construction for some special tree graph using adjacency matrix","authors":"Nikson Simarmata, Ikhlas Pratama Sandy, Kiki A. Sugeng","doi":"10.5614/ejgta.2023.11.2.1","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.1","url":null,"abstract":"In 1967, Rosa introduced β − labeling which was then popularized by Golomb under the name graceful. Graceful labeling on a graph G is an injective function f : V ( G ) → { 0 , 1 , 2 , . . . , | E ( G ) |} such that, when each edge uv ∈ E ( G ) is assigned the label | f ( u ) − f ( v ) | the resulting edge labels are distinct. If graph G has graceful labeling then G is called a graceful graph. Rosa also introduced α − labeling on graph G which is a graceful labeling f with an additional condition that there is λ ∈ { 1 , 2 , . . . , | E ( G ) |} so that for every edge uv ∈ E ( G ) where f ( u ) < f ( v ) then f ( u ) ≤ λ < f ( v ) . This paper gives a new approach to showing a graph is admitted α − labeling using an adjacency matrix. Then this construction will be used to construct graceful labeling for the superstar graph. Moreover, we give a graceful labeling construction for a super-rooted tree graph.","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"44 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322944","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
Signed graphs and signed cycles of hyperoctahedral groups 高八面体群的符号图和符号环
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.7
Ryo Uchiumi
{"title":"Signed graphs and signed cycles of hyperoctahedral groups","authors":"Ryo Uchiumi","doi":"10.5614/ejgta.2023.11.2.7","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.7","url":null,"abstract":"For a graph with edge ordering, a linear order on the edge set, we obtain a permutation of vertices by considering the edges as transpositions of endvertices. It is known from D'enes' results that the permutation of a tree is a full cyclic for any edge ordering. As a corollary, D'enes counted up the number of representations of a full cyclic permutation by means of product of the minimal number of transpositions. Moreover, a graph with an edge ordering which the permutation is a full cyclic is characterized by graph embedding. In this article, we consider an analogy of these results for signed graphs and hyperoctahedral groups. We give a necessary and sufficient condition for a signed graph to have an edge ordering such that the permutation is an even (or odd) full cyclic. We show that the edge ordering of the signed tree with some loops always gives an even (or odd) full cyclic permutation and count up the number of representations of an odd full cyclic permutation by means of product of the minimal number of transpositions.","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"7 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322950","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: 1
On the problems of CF-connected graphs 关于cf连通图的若干问题
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.12
Michal Staš, Juraj Valiska
{"title":"On the problems of CF-connected graphs","authors":"Michal Staš, Juraj Valiska","doi":"10.5614/ejgta.2023.11.2.12","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.12","url":null,"abstract":"The crossing number cr( G ) of a graph G is the minimum number of edge crossings over all drawings of G in the plane, and the optimal drawing of G is any drawing at which the desired minimum number of crossings is achieved. We conjecture that a complete graph K n is CF -connected if and only if it does not contain a subgraph of K 8 , where a connected graph G is CF -connected if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G . We establish the validity of this Conjecture for the complete graphs K n for any n ≤ 12 , and by assuming the Harary-Hill’s Conjecture that cr( K n ) = H ( n ) = 14 (cid:4) n 2 (cid:5)(cid:4) n − 1 2 (cid:5)(cid:4) n − 2 2 (cid:5)(cid:4) n − 3 2 (cid:5) is also valid for all n > 12 . The proofs of this paper are based on the idea of a new concept of a crossing sequence.","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"36 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322953","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 balance and consistency preserving 2-path signed graphs 关于保持平衡和一致性的2路有符号图
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.4
Kshittiz Chettri, Biswajit Deb, Anjan Gautam
{"title":"On balance and consistency preserving 2-path signed graphs","authors":"Kshittiz Chettri, Biswajit Deb, Anjan Gautam","doi":"10.5614/ejgta.2023.11.2.4","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.4","url":null,"abstract":"Let Σ = ( G, σ ) be a balanced and canonically consistent signed graph. The 2-path signed graph Σ#Σ = ( G 2 , σ ′ ) of Σ has the underlying graph as G 2 and the sign σ ′ ( uv ) of an edge uv in it is − 1 whenever in each uv -path of length 2 in Σ all edges are negative; otherwise σ ′ ( uv ) is 1 . Here, G 2 is the graph obtained from G by adding an edge between u and v if there is a path of length 2 between them. In this article, we have investigated balancedness and canonically consistency of 2-path signed graphs Σ#Σ of a balanced and canonically consistent signed graph Σ . The problem has been resolved completely for cycles, star graphs and trees.","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"33 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322960","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 dominating partition dimension and locating-chromatic number of graphs 图的主要划分维数和定位色数
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.10
Muhammad Ridwan, Hilda Assiyatun, Edy Tri Baskoro
{"title":"The dominating partition dimension and locating-chromatic number of graphs","authors":"Muhammad Ridwan, Hilda Assiyatun, Edy Tri Baskoro","doi":"10.5614/ejgta.2023.11.2.10","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.10","url":null,"abstract":"For every graph G , the dominating partition dimension of G is either the same as its partition dimension or one higher than its partition dimension. In this paper, we consider some general connections among these three graph parameters: partition dimension, locating-chromatic number, and dominating partition dimension. We will show that β p ( G )≤ η p ( G )≤ χ L ( G ) for any graph G with at least 3 vertices. Therefore, we will derive properties for which graphs G have η p ( G )= β p ( G ) or η p ( G )= β p ( G )+1 .","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135321971","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
(1, 2)-rainbow connection number at most 3 in connected dense graphs (1,2)-彩虹连接数在连通密集图中最多为3个
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.6
Trung Duy Doan, Le Thi Duyen
{"title":"(1, 2)-rainbow connection number at most 3 in connected dense graphs","authors":"Trung Duy Doan, Le Thi Duyen","doi":"10.5614/ejgta.2023.11.2.6","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.6","url":null,"abstract":"Let G be an edge-colored connected graph G . A path P in the graph G is called l -rainbow path if each subpath of length at most l + 1 is rainbow. The graph G is called ( k, l ) -rainbow connected if any two vertices in G are connected by at least k pairwise internally vertex-disjoint l -rainbow paths. The smallest number of colors needed in order to make G ( k, l ) -rainbow connected is called the ( k, l ) -rainbow connection number of G and denoted by rc k,l ( G ) . In this paper, we consider the (1 , 2) -rainbow connection number at most 3 in some connected dense graphs. Our main results are as follows: (1) Let n ≥ 7 be an integer and G be a connected graph of order n . If ω ( G ) ≥ n − 3 , then rc 1 , 2 ( G ) ≤ 3 . Moreover, the bound of the clique number is sharpness. (2) Let n ≥ 7 be an integer and G be a connected graph of order n . If | E ( G ) | ≥ (cid:0) n − 3 2 (cid:1) + 7 , then rc 1 , 2 ( G ) ≤ 3 .","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"62 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322956","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
Variations on Ramsey numbers and minimum numbers of monochromatic triangles in line $2$-colorings of configurations 拉姆齐数的变化和第2行单色三角形的最小数目——构型的着色
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.8
Jamie Bishop, Rebekah Kuss, Benjamin Peet
{"title":"Variations on Ramsey numbers and minimum numbers of monochromatic triangles in line $2$-colorings of configurations","authors":"Jamie Bishop, Rebekah Kuss, Benjamin Peet","doi":"10.5614/ejgta.2023.11.2.8","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.8","url":null,"abstract":"This paper begins by exploring some old and new results about Ramsey numbers and minimum numbers of monochromatic triangles in 2 -colorings of complete graphs, both in the disjoint and non-disjoint cases. We then extend the theory, by defining line 2 -colorings of configurations of points and lines and considering the minimum number of non-disjoint monochromatic triangles. We compute specific examples for notable symmetric v 3 configurations before considering a general result regarding the addition or connected sum of configurations through incidence switches. The paper finishes by considering the maximal number of mutually intersecting lines and how this relates to the minimum number of triangles given a line 2 -coloring of a symmetric v 3 configuration.","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"20 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322943","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 matching number, decomposition and representation of well-formed graph 关于良构图的匹配数、分解和表示
Electronic Journal of Graph Theory and Applications Pub Date : 2023-10-24 DOI: 10.5614/ejgta.2023.11.2.13
Alex Ralph Baisa Nieva, Karen P. Nocum
{"title":"On matching number, decomposition and representation of well-formed graph","authors":"Alex Ralph Baisa Nieva, Karen P. Nocum","doi":"10.5614/ejgta.2023.11.2.13","DOIUrl":"https://doi.org/10.5614/ejgta.2023.11.2.13","url":null,"abstract":"In this paper, we find a special type of non-traceable cubic bridge graph called well-formed graph whose central fragment is isomorphic to a hairy cycle and whose branches are pairwise isomorphic. We then show that a well-formed graph can be partition into isomorphic subgraph. Some properties of a well-formed graph such as perfect matching, matching number, decomposition and some parameters for pictorial representation are also provided","PeriodicalId":43771,"journal":{"name":"Electronic Journal of Graph Theory and Applications","volume":"BME-14 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135322951","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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