摘要
Ｇ是ｎ个顶点ｍ条边的简单图，Ｇ是Ｇ的补图，δ和Δ分别是图Ｇ的最小次和最大次，λ１（Ｇ）和λ１（Ｇ）分别是Ｇ和Ｇ的谱半径．本文将证明λ１（Ｇ）＋λ１（Ｇ）满足以下不等式①λ１（Ｇ）＋λ１（Ｇ）≤－１＋１＋２ｎ（ｎ－１）－４δ（ｎ－１－Δ）②若Ｇ与Ｇ均无孤立点，则有λ１（Ｇ）＋λ１（Ｇ）≤２（ｎ－１）（ｎ－２）
Let G be a simple graph with n vertices and m edges. be the complement graph of G , δ and Δ denote the minimum and maximum degree of the graph G respectively. λ 1(G) and λ 1() denote the spectral radius of the graph G and its complements graph . In this paper we proved that λ 1(G)+λ 1() satisfies following inequality ① λ 1(G)+λ 1()≤-1+2n(n-1)+1-4δ(n-1-Δ) ② If G and without isolated vertices, all λ 1(G)+λ 1()≤2(n-1)(n-2).
出处
《华北工学院学报》
1996年第4期297-299,共3页
Journal of North China Institute of Technology
关键词
邻接矩阵
谱半径
图论
adjacency matrix
complement graph
spectral radius
