Nonregular Graphs with Three Eigenvalues
نویسندگان
چکیده
منابع مشابه
Extreme eigenvalues of nonregular graphs
Let λ1 be the greatest eigenvalue and λn the least eigenvalue of the adjacency matrix of a connected graph G with n vertices, m edges and diameter D. We prove that if G is nonregular, then Δ− λ1 > nΔ− 2m n(D(nΔ− 2m)+ 1) 1 n(D + 1) , where Δ is the maximum degree of G. The inequality improves previous bounds of Stevanović and of Zhang. It also implies that a lower bound on λn obtained by Alon an...
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We consider undirected non-regular connected graphs without loops and multiple edges (other than complete bipartite graphs) which have exactly three distinct eigenvalues (such graphs are called non-standard graphs). The interest in these graphs is motivated by the questions posed by W. Haemers during the 15th British Combinatorial Conference (Stirling, July 1995); the main question concerned th...
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Let G be a graph of order n with (0, 1)-adjacency matrix A. An eigenvalue σ of A is said to be an eigenvalue of G, and σ is a main eigenvalue if the eigenspace EA(σ) is not orthogonal to the all-1 vector in IR. Always the largest eigenvalue, or index, of G is a main eigenvalue, and it is the only main eigenvalue if and only if G is regular. We say that G is an integral graph if every eigenvalue...
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Article history: Received 13 June 2008 Accepted 13 November 2008 Available online xxxx Submitted by R.A. Brualdi AMS classification: 05C50
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1998
ISSN: 0095-8956
DOI: 10.1006/jctb.1998.1815