On the Laplacian spectral radius of a graph
نویسندگان
چکیده
Let G be a simple graph with n vertices and m edges and Gc be its complement. Let δ(G) = δ and (G) = be the minimum degree and the maximum degree of vertices of G, respectively. In this paper, we present a sharp upper bound for the Laplacian spectral radius as follows: λ1(G) ( + δ − 1)+ √ ( + δ − 1)2 + 4(4m− 2δ(n− 1)) 2 . Equality holds if and only if G is a connected regular bipartite graph. Another result of the paper is an upper bound for the Laplacian spectral radius of the Nordhaus–Gaddum type. We prove that λ1(G)+ λ1(G) n− 2 + √ ( + δ + 1 − n)2 + n2 + 4( − δ)(n− 1). © 2003 Elsevier Inc. All rights reserved.
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تاریخ انتشار 2003