Results 11 to 20 of about 64,086 (307)
Domatically perfect graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 A graph of order is domatically perfect if , where and denote the domination number and the domatic number, respectively. In this paper, we give basic results for domatically perfect graphs, and study a main problem; for a given graph , to find a ...
Naoki Matsumoto
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Contractions in perfect graphs
Discrete Applied MathematicsIn this paper, we characterize the class of {\em contraction perfect} graphs which are the graphs that remain perfect after the contraction of any edge set. We prove that a graph is contraction perfect if and only if it is perfect and the contraction of any single edge preserves its perfection.
Alexandre Dupont-Bouillard +3 more
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Perfect double Italian domination of a graph
AKCE International Journal of Graphs and Combinatorics, 2023 For a graph [Formula: see text] with [Formula: see text] and [Formula: see text], a perfect double Italian dominating function is a function [Formula: see text] having the property that [Formula: see text], for every vertex [Formula: see text] with ...
Guoliang Hao +2 more
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On the perfect graph conjecture
Discrete Mathematics, 1976 We prove the following theorem: If every, odd cycle of length ≥5 has at least two chords, then the graph is perfect. This generalizes a result of Gallai and Suranyi and also a result of Olaru and Sachs.
Meyniel, H.
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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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Perfect Nilpotent Graphs [PDF]
Kragujevac Journal of Mathematics, 2021 Let R be a commutative ring with identity. The nilpotent graph of R, denoted by ΓN(R), is a graph with vertex set ZN(R)∗, and two vertices x and y are adjacent if and only if xy is nilpotent, where ZN(R) = {x ∈ R∣xy is nilpotent, for some y ∈ R∗}. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the ...
Nikmehr, M. J., Azadi, A.
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Journal of Combinatorial Theory, Series B, 2018 Let $G=(V,E)$ be a graph and let $A_G$ be the clique-vertex incidence matrix of $G$. It is well known that $G$ is perfect iff the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$ is totally dual integral (TDI). In 1982, Cameron and Edmonds proposed to call $G$ box-perfect if the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$
Guoli Ding, Wenan Zang, Qiulan Zhao
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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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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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