Bounds of graph energy in terms of vertex cover number

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• 作者：Long Wang ; ^{wanglongxuzhou@163.com} ; Xiaobin Ma
• 关键词：05C20 ; 05C50 ; 05C75
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：517
• 期：Complete
• 页码：207-216
• 全文大小：297 K
• 卷排序：517

文摘

The energy E(G)E(G) of a graph G is the sum of the absolute values of all eigenvalues of G. In this paper, we give a lower bound and an upper bound for graph energy in terms of vertex cover number. For a graph G with vertex cover number τ  , it is proved that 2τ−2c≤E(G)≤2τΔ, where c is the number of odd cycles in G and Δ is the maximum vertex degree of G. The lower bound is attained if and only if G is the disjoint union of some complete bipartite graphs with perfect matchings and some isolated vertices, the upper bound is attained if and only if G is the disjoint union of τ   copies of K1,ΔK1,Δ together with some isolated vertices.