Bounds for the matching number, the edge chromatic number and the independence number of a graph in terms of rank

被引：51
|
作者：
Wang, Long [1 ]
Wong, Dein [1 ]
机构：
[1] China Univ Min & Technol, Dept Math, Xuzhou 221116, Peoples R China
来源：
DISCRETE APPLIED MATHEMATICS | 2014年 / 166卷
基金：
中国国家自然科学基金;
关键词：
Rank of graphs; Matching number; Chromatic index; Independence number; NULLITY; TREES;
D O I：
10.1016/j.dam.2013.09.012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G = (V, E) be a simple graph with vertex set V and edge set E. The rank of G, written as r, is defined to be the rank of its adjacency matrix. Let c denote e-nu+theta where e = vertical bar E vertical bar, nu = vertical bar V vertical bar and theta means the number of connected components of G, and let m, a, x' respectively be the matching number, the independence number, and the chromatic index of G. In this paper, it is proved that [r-c/2] <= m <= [r+2c/2], [2e/r+2c] <= X', and v-[r/2]-c <= alpha <= v- [r/2] Examples are given to show that all the bounds can be attained. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码：276 / 281
页数：6
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