On Laplacian-energy-like invariant of a graph <
On Laplacian-energy-like invariant of a graph <
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DOI：
10.1016/j.laa.2012.03.004
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发表时间：
2012-07
影响因子：
1.1
通讯作者：
Weizhong Wang;Yanfeng Luo
中科院分区：
文献类型：
--
作者：
Weizhong Wang;Yanfeng Luo
设G是n阶简单图，μ1≥μ2≥μn ≥μn=0是G的Laplacian谱. G的类拉普拉斯能量不变量（简称LEL）定义为LEL（G）=∑i= 1 n-1μi.本文用最大度给出了图的LEL的一个新的下界。同时，给出了线图的LEL的上界和下界（分别为，得到了正则图G的剖分图和全图。
Let G be a simple graph of order n, and let μ1≥μ2≥⋯≥μn=0 be the Laplacian spectrum of G. The Laplacian-energy-like invariant of G (LEL for short) is defined as LEL(G)=∑i=1n-1μi. In this paper, a new lower bound for LEL of graphs in terms of the maximum degree is given. Meanwhile, an upper bound and a lower bound for LEL of the line graph (resp., the subdivision graph and the total graph) of a regular graph G are obtained.