Some Upper Bounds for the Laplacian Spectral Radius of the Nordhaus-Gaddum Type
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چکیده
Let G be a simple graph with n vertices, and let G 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, some upper bounds for the Laplacian spectral radius of the Nordhaus-Gaddum type are obtained as follows: λ1(G) + λ1(G) ≤ 3n+∆− δ − 5 + √ 2(n+∆)2 + 2(δ + 1)2 − 8nδ 2 , λ1(G) + λ1(G) ≤ n+∆− δ − 1 + √( 2− 1 ω(G) − 1 ω(Gc) ) n(n− 1)
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تاریخ انتشار 2004