一些图的拟拉普拉斯能量和基尔霍夫指标（英文）

The Laplacian-Energy-Like Invariant and the Kirchhoff Index of some Graphs

G是具有拉普拉斯特征值μ1≥μ2≥···≥μn=0的的n阶连通图.G的拟拉普拉斯能量和基尔霍夫指标分别定义为LEL=∑n-1i=1√μi和Kf=n∑n-1i=11/μi.本文研究半正则图的线图及正则图细分图的线图,给出这两类图的拟拉普拉斯能量和基尔霍夫指标的界,同时获得它们的基尔霍夫指标公式.

Let G be a connected graph of order n with Laplacian eigenvalues itμ1≥μ2≥···≥μn=0. The Laplacian-energy-like invariant （LEL for short） and theKirchhoff index of G are defined as LEL=∑n-1i=1√μi和Kf=n∑n-1i=11/μi, respeclvety. In this paper, bounds for LEL and Kf of the line graph of a semiregular graph and the para-line graph of a regular graph are given. In addition, formulae for Kf of these two classes graphs are obtained.