Bounds of graph energy in terms of vertex cover number
Bounds of graph energy in terms of vertex cover number
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DOI：
10.1016/j.laa.2016.12.015
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发表时间：
2017-03
影响因子：
1.1
通讯作者：
Long Wang;Xiaobin Ma
中科院分区：
文献类型：
--
作者：
Long Wang;Xiaobin Ma
图G的能量E（G）是图G的所有特征值的绝对值之和。本文利用顶点覆盖数给出了图能量的一个上界和一个下界。对于顶点覆盖数为τ的图G，证明了2 τ− 2 c≤ E（G）≤ 2 τ Δ，其中c是G中奇圈的个数，Δ是G的最大顶点度.得到了下界的充分必要条件是G是具有完美匹配的完全二部图与孤立点的不交并，得到了上界的充分必要条件是G是K1，Δ的τ个副本与孤立点的不交并.
The energy 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 2 τ− 2 c≤ E (G)≤ 2 τ Δ, 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 K 1, Δ together with some isolated vertices.