Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.2
Frances Dean, Max Everett, Ralph Morrison
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.
{"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}
Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.9
Joshua Lambert, Michael Tiemeyer
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.
{"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}
Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.1
Nikson Simarmata, Ikhlas Pratama Sandy, Kiki A. Sugeng
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.
{"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}
Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.7
Ryo Uchiumi
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.
{"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}
Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.12
Michal Staš, Juraj Valiska
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.
{"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}
Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.4
Kshittiz Chettri, Biswajit Deb, Anjan Gautam
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.
{"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}
Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.10
Muhammad Ridwan, Hilda Assiyatun, Edy Tri Baskoro
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 .
对于每一个图G, G的主导划分维数要么等于它的划分维数，要么比它的划分维数高一个。本文考虑了图的划分维数、定位色数和主导划分维数这三个参数之间的一般联系。我们将证明β p (G)≤η p (G)≤χ L (G)对于任何至少有3个顶点的图G。因此，我们将推导出图G具有η p (G)= β p (G)或η p (G)= β p (G)+1的性质。
{"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}
Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.6
Trung Duy Doan, Le Thi Duyen
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 .
{"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}
Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.8
Jamie Bishop, Rebekah Kuss, Benjamin Peet
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.
{"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}
Pub Date : 2023-10-24DOI: 10.5614/ejgta.2023.11.2.13
Alex Ralph Baisa Nieva, Karen P. Nocum
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
{"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}
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