华东师范大学学报（自然科学版） >

2015 , Vol. 2015 >Issue 1: 136 - 141

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.01.017

应用数学与基础数学

图的极大匹配能(英)

  • 吴廷增
展开
  • 青海民族大学 数学与统计学院, 西宁 810007

收稿日期: 2014-05-01

  网络出版日期: 2015-03-29

基金资助

青海民族大学重点学科建设项目和校级项目(2015XJZ03)

收起

On the maximal matching energy of graphs

  • WU Ting-Zeng
Expand
  • School of Mathematics and Statistics, Qinghai Nationalities University, Xining 810007, China

Received date: 2014-05-01

  Online published: 2015-03-29

Fold

摘要

Gutman和Wagner (The matching energy of a graph, Discrete Appl. Math. 2012 (160): 2177-2187)首次提出了匹配能的定义, 即:图的匹配多项式的所有特征根的绝对值之和称为图的匹配能.他们证明了在n个顶点的图中, 完全图$K_{n}$有最大匹配能.本文完全刻画了具有第二大至第十六大匹配能的图

关键词： 匹配多项式; 匹配能; Hosoya指标

本文引用格式

吴廷增 . 图的极大匹配能(英)[J]. 华东师范大学学报（自然科学版）, 2015 , 2015(1) : 136 -141 . DOI: 10.3969/j.issn.1000-5641.2015.01.017

Abstract

The matching energy is defined as the sum of the absolute values of the zeros
of the matching polynomial of a graph, which was firstly proposed by Gutman and Wagner
(The matching energy of a graph, Discrete Appl. Math. 2012 (160): 2177õ2187). And
they showed that the complete graph Kn had maximum matching energy in all graphs on
n vertices. In this paper, among all graphs on n vertices, the graphs with i-th maximal
matching energy are completely characterized, where i = 2, 3, . . . , 16.

Key words： matching polynomial; matching energy; Hosoya index

参考文献

GODSIL C D.  Algebraic Combinatorics [M]. New York: Chapman and Hall, 1993.
GUTMAN I, WAGNER S.  The matching energy of a graph [J]. Discrete Appl Math, 2012 (160): 2177--2187.
JI S J, LI X L, SHI Y T. Extremal matching energy of bicyclic graphs [J]. MATCH Commun Math Comput Chem, 2013 (70): 697--706.
LI S L, YAN W G. The matching energy of graphs with given parameters [J]. Discrete Appl Math, 2014 (162): 415--420.
ZHANG H P, WU T Z, LAI H J. Per-spectral characterizations of some edge-deleted subgraphs of  a complete graph [J]. Linear and Multilinear Algebra, 2015 (63): 397-410.
LOVASZ L. Combinatorial Problems and Exercises [M]. Akadémiai Kiadó: Budapest,  1993. MOHAR B. Some applications of Laplace eigenvalues of graphs [M]//HAHN G, EDS G S. Graph Symmetry. Dordrecht: Kluwer Academic Press, 1997, 225-275.
CAO D S, HONG Y. The distribution of eigenvalues of graphs [J]. Linear Algebra and its Application, 1995 (216): 211-224.
SHEARER J B. On the distribution of the maximum eigenvalue of graphs [J]. Linear Algebra and its Application, 1984 (114/115): 17-20.
GUO J M. The limit points of Laplacian spectra of graphs [J]. Linear Algebra and its Application, 2003 (362): 121-128.
GUO J M. On limit points of Laplacian spectral radii of graphs [J]. Linear Algebra and its Application, 2008 (429): 1705-1718.
SHU J L. Bounds on Eigenvalues of Graphs (in Chinese) [D]. Shanghai: East China Normal University, 1999.
VO\'ASZ L, PELINK\'AN J. On the eigenvalues of tress [J]. Periodica Math Hung 1973 (3): 175-182.
DOOB M. The limit points of eigenvalues of graphs [J]. Linear Algebra and its Application, 1989 (114/115): 659-662.
GRONE R, MERRIS R, SUNDER V. The Laplacian spetrum of a graph [J]. SIAM J Matrix Anal Appl, 1990 (11): 218-238.
MERRIS R. Laplacian matrices of graphs:a surver [J]. Linear Algebra and its Application, 1994 (197/198): 143-176.
ZHANG X D. Graphs with fourth Laplacian eigenvalue less than two [J]. European Journal of Combinatorics, 2003 (24): 617-630.
Options
文章导航

/

〈 〉