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On co-maximal subgroup graph of $Z_n$ [PDF]
International Journal of Group Theory, 2022 The co-maximal subgroup graph $\Gamma(G)$ of a group $G$ is a graph whose vertices are non-trivial proper subgroups of $G$ and two vertices $H$ and $K$ are adjacent if $HK = G$.
Manideepa Saha +2 more
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Total perfect codes in graphs realized by commutative rings [PDF]
Transactions on Combinatorics, 2022 Let $R$ be a commutative ring with unity not equal to zero and let $\Gamma(R)$ be a zero-divisor graph realized by $R$. For a simple, undirected, connected graph $G = (V, E)$, a {\it total perfect code} denoted by $C(G)$ in $G$ is a subset $C(G ...
Rameez Raja
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Parameters of the coprime graph of a group [PDF]
International Journal of Group Theory, 2021 There are many different graphs one can associate to a group. Some examples are the well-known Cayley graph, the zero divisor graph (of a ring), the power graph, and the recently introduced coprime graph of a group.
Jessie Hamm, Alan Way
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Fractional matching preclusion for generalized augmented cubes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 The \emph{matching preclusion number} of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings.
Tianlong Ma +3 more
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Two short proofs of the Perfect Forest Theorem
Theory and Applications of Graphs, 2017 A perfect forest is a spanning forest of a connected graph $G$, all of whose components are induced subgraphs of $G$ and such that all vertices have odd degree in the forest.
Yair Caro, Josef Lauri, Christina Zarb
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On two consequences of Berge–Fulkerson conjecture
AKCE International Journal of Graphs and Combinatorics, 2020 The classical Berge–Fulkerson conjecture states that any bridgeless cubic graph admits a list of six perfect matchings such that each edge of belongs to two of the perfect matchings from the list.
Vahan V. Mkrtchyan, Gagik N. Vardanyan
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Perfect Fuzzy Soft Tripartite Graphs and Their Complements
Discrete Dynamics in Nature and Society, 2022 Fuzzy soft graphs are efficient numerical tools for simulating the uncertainty of the real world. A fuzzy soft graph is a perfect fusion of the fuzzy soft set and the graph model that is widely used in a variety of fields.
Kalaichelvan Kalaiarasi +4 more
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A semi-strong perfect digraph theorem
AKCE International Journal of Graphs and Combinatorics, 2020 Reed (1987) showed that, if two graphs are P4-isomorphic, then either both are perfect or none of them is. In this note, we will derive an analogous result for perfect digraphs.
Stephan Dominique Andres +3 more
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Systems with the integer rounding property in normal monomial subrings
Anais da Academia Brasileira de Ciências, 2010 Let C be a clutter and let A be its incidence matrix. If the linear system x > 0; x A < 1 has the integer rounding property, we give a description of the canonical module and the a-invariant of certain normal subrings associated to C. If the clutter is a
Luis A. Dupont +2 more
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Tight upper bound on the maximum anti-forcing numbers of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Let $G$ be a simple graph with a perfect matching. Deng and Zhang showed that the maximum anti-forcing number of $G$ is no more than the cyclomatic number.
Lingjuan Shi, Heping Zhang
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