منابع مشابه
D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs
The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...
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We study partially distance-regular graphs and partially walkregular graphs as generalizations of distance-regular graphs and walkregular graphs respectively. We conclude that the partially distanceregular graphs can be viewed as some extremal graphs of partially walk-regular graphs. In the special case that the graph is assumed to be regular with four distinct eigenvalues, a well known class o...
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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The integrity of a graph G, I(G), is defined by I(G) = minS⊆V (G){|S| + m(G − S)} where m(G− S) is the maximum order of the components of G− S. In general the integrity of r-regular graph is not known [?]. We answer the following question for special regular graphs. For any given two integers p and r such that pr 2 is an integer, is there a r-regular graph, say G ∗, on p vertices having size q ...
متن کاملEMBEDDING /c-REGULAR GRAPHS IN /c +1-REGULAR GRAPHS
Given a A:-regular graph G of order n, what is the minimum number v(G) of extra vertices required to embed G in a /<+1-regular graph? Clearly v(G) = 0 precisely when the complement G of G has a 1-factor—in particular, when n ^ 2k is even. Suppose G has no 1-factor: if n, k have opposite parity we show that v(G) = 1, while if n, k have the same parity (which must then be even with n < 2k) we sho...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1975
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700020735