منابع مشابه
Pan-Factorial Property in Regular Graphs
Among other results, we show that if for any given edge e of an r-regular graph G of even order, G has a 1-factor containing e, then G has a k-factor containing e and another one avoiding e for all k, 1 ≤ k ≤ r − 1. Submitted: Nov 4, 2004; Accepted: Nov 7, 2005; Published: Nov 15, 2005 MSC: 05C70, 05C75.
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Let Γ denote a Q-polynomial distance-regular graph with diameter D ≥ 4. Assume that the intersection numbers of Γ satisfy ai = 0 for 0 ≤ i ≤ D − 1 and aD 6= 0. We show that Γ is a polygon, a folded cube, or an Odd graph.
متن کاملA New Property of Random Regular Bipartite Graphs
One deals with r-regular bipartite graphs with 2n vertices. In a previous paper Butera, Pernici, and the author have introduced a quantity d(i), a function of the number of imatchings, and conjectured that as n goes to infinity the fraction of graphs that satisfy ∆d(i) ≥ 0, for all k and i, approaches 1. Here ∆ is the finite difference operator. In this paper it is proved that for each r, i, an...
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We explore an operation on graphs that is analogous to the factorial of a positive integer. We develop formulas for the factorials of complete graphs, odd cycles and complete bipartite graphs, and we prove some properties of the factorial operation. We conclude with a list of open questions. This paper explores some properties of a factorial operation that associates to each graph G a graph G! ...
متن کاملRegular factors in regular graphs
Katerinis, P., Regular factors in regular graphs, Discrete Mathematics 113 (1993) 269-274. Let G be a k-regular, (k I)-edge-connected graph with an even number of vertices, and let m be an integer such that 1~ m s k 1. Then the graph obtained by removing any k m edges of G, has an m-factor. All graphs considered are finite. We shall allow graphs to contain multiple edges and we refer the reader...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2005
ISSN: 1077-8926
DOI: 10.37236/1990