Regular Factors of Regular Graphs from Eigenvalues
نویسندگان
چکیده
منابع مشابه
Regular Factors of Regular Graphs from Eigenvalues
Let r and m be two integers such that r > m. Let H be a graph with order |H|, size e and maximum degree r such that 2e > |H|r−m. We find a best lower bound on spectral radius of graph H in terms of m and r. Let G be a connected r-regular graph of order |G| and k < r be an integer. Using the previous results, we find some best upper bounds (in terms of r and k) on the third largest eigenvalue th...
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Throughout, G denotes a simple graph of order n (the number of vertices) and size e (the number of edges). The eigenvalues of G are the eigenvalues λi 1 Research partially supported by an NSERC postdoctoral fellowship. 2 Research supported by the Natural Sciences and Engineering Research Council of Canada. Email addresses: [email protected] (Sebastian M. Cioabă), [email protected] (D...
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Article history: Received 6 December 2006 Available online 26 July 2008
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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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In this paper, we show that if the second largest eigenvalue of a d-regular graph is less than d − 2(k−1) d+1 , then the graph is k-edge-connected. When k is 2 or 3, we prove stronger results. Let ρ(d) denote the largest root of x3 − (d− 3)x2 − (3d− 2)x− 2 = 0. We show that if the second largest eigenvalue of a d-regular graph G is less than ρ(d), then G is 2-edge-connected and we prove that if...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/431