منابع مشابه
Counting perfect matchings of cubic graphs in the geometric dual
Lovász and Plummer conjectured, in the mid 1970’s, that every cubic graph G with no cutedge has an exponential in |V (G)| number of perfect matchings. In this work we show that every cubic planar graph G whose geometric dual graph is a stack triangulation has at least 3φ (G)|/72 distinct perfect matchings, where φ is the golden ratio. Our work builds on a novel approach relating Lovász and Plum...
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We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
متن کاملTotal perfect codes, OO-irredundant and total subdivision in graphs
Let $G=(V(G),E(G))$ be a graph, $gamma_t(G)$. Let $ooir(G)$ be the total domination and OO-irredundance number of $G$, respectively. A total dominating set $S$ of $G$ is called a $textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$. In this paper, we show that if $G$ has a total perfect code, then $gamma_t(G)=ooir(G)$. As a consequence, ...
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ژورنال
عنوان ژورنال: Moscow Mathematical Journal
سال: 2015
ISSN: 1609-3321,1609-4514
DOI: 10.17323/1609-4514-2015-15-2-319-335