RELATIONSHIP BETWEEN THE SPECTRAL RADIUS  OF GRAPHS AND ITS COMPLEMENTS

李秀兰

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RELATIONSHIP BETWEEN THE SPECTRAL RADIUS OF GRAPHS AND ITS COMPLEMENTS

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- RELATIONSHIP BETWEEN THE SPECTRAL RADIUS OF GRAPHS AND ITS COMPLEMENTS
- 图与其补图的谱半径之间的关系
- Issue 4, (1996)
- 作者机构：
  
  雁北师范学院
- 作者简介：
- 基金信息：
- DOI：
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- Published：1996
- 稿件说明：
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李秀兰. RELATIONSHIP BETWEEN THE SPECTRAL RADIUS OF GRAPHS AND ITS COMPLEMENTS[J]. 1996, (4).
DOI：

李秀兰. RELATIONSHIP BETWEEN THE SPECTRAL RADIUS OF GRAPHS AND ITS COMPLEMENTS[J]. 1996, (4). DOI：

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）

Abstract

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).

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