منابع مشابه
The Excessive [3]-Index of All Graphs
Let m be a positive integer and let G be a graph. A set M of matchings of G, all of which of size m, is called an [m]-covering of G if ⋃ M∈MM = E(G). G is called [m]-coverable if it has an [m]-covering. An [m]-covering M such that |M| is minimum is called an excessive [m]-factorization of G and the number of matchings it contains is a graph parameter called excessive [m]-index and denoted by χ[...
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The harmonic index of a graph $G$, denoted by $H(G)$, is defined asthe sum of weights $2/[d(u)+d(v)]$ over all edges $uv$ of $G$, where$d(u)$ denotes the degree of a vertex $u$. Hu and Zhou [Y. Hu and X. Zhou, WSEAS Trans. Math. {bf 12} (2013) 716--726] proved that for any bicyclic graph $G$ of order $ngeq 4$, $H(G)le frac{n}{2}-frac{1}{15}$ and characterize all extremal bicyclic graphs.In this...
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Vizing has shown that if G is a simple graph with maximum vertex-degree p, then the chromatic index of G is either p or p + 1 . In this note we prove that almost all graphs have a unique vertex of maximum degree, and we deduce that almost all graphs have chromatic index equal to their maximum degree . This settles a conjecture of the second author (in "Proceedings of the Fifth British Combinato...
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For an integer s > 0 and for u, v ∈ V (G) with u = v, an (s; u, v)-pathsystem of G is a subgraph H of G consisting of s internally disjoint (u, v)-paths, and such an H is called a spanning (s; u, v)-path system if V (H) = V (G). The spanning connectivity κ∗(G) of graph G is the largest integer s such that for any integer k with 1 ≤ k ≤ s and for any u, v ∈ V (G) with u = v, G has a spanning (k;...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/213