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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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Dual Perfect Bases and Dual Perfect Graphs [PDF]
Moscow Mathematical Journal, 2015 We introduce the notion of dual perfect bases and dual perfect graphs. We show that every integrable highest weight module $V_q( )$ over a quantum generalized Kac-Moody algebra $U_{q}(\mathcal{g})$ has a dual perfect basis and its dual perfect graph is isomorphic to the crystal $B( )$.
Byeong Hoon Kahng +3 more
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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 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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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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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 $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$
Zang, W, ZHAO, Q, Ding, G
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INDUCED REGULAR PERFECT GRAPHS
South East Asian J. of Mathematics and Mathematical Sciences, 2023 A graph G is said to be R-perfect if, for all induced subgraphs H of G, the induced regular independence number of each induced subgraph H is equal to its corresponding induced regular cover. Here, the induced regular independence number is the maximum number of vertices in H such that no two belong to the same induced regular subgraph in H, and the ...
Jayakumar, Gokul S., V., Sangeetha
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Square-free perfect graphs [PDF]
Journal of Combinatorial Theory, Series B, 2004 We prove that square-free perfect graphs are bipartite graphs or line graphs of bipartite graphs or have a 2-join or a star cutset.
CONFORTI, MICHELANGELO +2 more
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