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Journal of Combinatorial Theory Series B, 2005 Graphs of high girth have been much studied, especially in the context of the minimum vertex number of graphs of given girth and minimum degree. The authors study the treewidth \(\text{tw}(G)\) of a graph \(G\), giving a lower bound in terms of the girth \(g(G)\) and average degree \(d(G)\). They show that \[ \text{tw}(G)\geq c {1\over g(G)+1} (d(G)-1)^
Chandran, L., Subramanian, C.
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A GRAPH ASSOCIATED TO ESPECIAL ESSENTIALITY OF SUBMODULES [PDF]
Journal of Algebraic Systems, 2023 Let $R$ be an associative ring with identity. In this paper weassociate to every $R$-module $M$ a simple graph $\Gamma_e(M)$, which we call it the essentiality graph of $M$.
Mehdi Ebrahimi Dorcheh, Saeid Bagheri
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A stability result for girth‐regular graphs with even girth [PDF]
Journal of Graph Theory, 2021 AbstractLet denote a finite, connected, simple graph. For an edge of let denote the number of girth cycles containing . For a vertex of let be the set of edges incident to ordered such that . Then is called the signature of . The graph is said to be girth‐regular if all of its vertices have the same signature.
György Kiss +2 more
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ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP
Barekeng, 2023 The coprime graph of a finite group , denoted by , is a graph with vertex set such that two distinct vertices and are adjacent if and only if their orders are coprime, i.e., where |x| is the order of x.
Agista Surya Bawana +2 more
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Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, 2011 This article considers the problem of computing a minimum weight cycle in weighted undirected graphs. Given a weighted undirected graph G = ( V , E , w ), let C be a minimum weight cycle of G , let
Liam Roditty, Roei Tov
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4-CYCLE FREE APM LDPC CODES WITH AN EXPLICIT CONSTRUCTION [PDF]
Journal of Algebraic Systems, 2021 Recently, a class of low-density parity-check codes based on affine permutation matrices, called APM-LDPC codes, have been considered which have some advantages than quasi-cyclic (QC) LDPC codes in terms of minimum-distance, cycle distribution, and error-
Z. Gholami, M. Gholami
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Journal of Graph Theory, 1980 AbstractFor an integer k > 2, the best function m(n, k) is determined such that every strong digraph of order n with at least m(n, k) arcs contains a circuit of length k or less.
Jean-Claude Bermond +3 more
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A REDUCTION IN THE SEARCH SPACE OF QC-LDPC CODES WITH GIRTH 8 [PDF]
Journal of Algebraic Systems, 2020 In this paper, we define a structure to obtain exponent matrices of girth-8 QC-LDPC codes with column weight 3. Using the difference matrices introduced by Amirzade et al., we investigate necessary and sufficient conditions which result in a Tanner graph
F. Amirzade +2 more
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Some properties of semiregular cages [PDF]
Discrete Mathematics & Theoretical Computer Science, 2010 Graphs and ...
Camino Balbuena +2 more
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Coloring Powers and Girth [PDF]
SIAM Journal on Discrete Mathematics, 2016 15 pages, 2 figures, 2 tables; from v1 to v2, one section removed, one theorem ...
Kang, J.R., Kang, J.R., Pirot, F.F.
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