On the maximal matching energy of graphs

doi:10.3969/j.issn.1000-5641.2015.01.017

Abstract

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 K_n 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

CLC Number:

O157.5

WU Ting-Zeng. On the maximal matching energy of graphs[J]. Journal of East China Normal University(Natural Sc, 2015, 2015(1): 136-141.

References

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.

[1]	MA Hua, JIANG Xue-Zhong. In consideration of tidal condition to improve optical inversion algorithm on total suspended matters concentration according to in situ measurement in the Yangtze Estuary [J]. Journal of East China Normal University(Natural Sc, 2016, 2016(3): 146-155.
[2]	XU Yang. List improper coloring of graphs of nonnegative characteristic [J]. Journal of East China Normal University(Natural Sc, 2016, 2016(2): 51-55.
[3]	HE Chang-Xiang, LIU Wei-Long. Minimum fundamental cycle basis of (n-2)-regular bipartite graphs with order 2n [J]. Journal of East China Normal University(Natural Sc, 2016, 2016(2): 56-61.
[4]	NIU Ai-Hong, WANG Guo-Ping, QIN Zheng-Xin, MOU Shan-Zhi. Characterization of bipartite graph with maximum spectral radius [J]. Journal of East China Normal University(Natural Sc, 2016, 2016(1): 96-101.
[5]	HUANG Xiao-Jia, CHEN Xiang-恩, WANG Zhi-Wen. d-strong total colorings of cycles when 35<=d<=55 [J]. Journal of East China Normal University(Natural Sc, 2015, 2015(6): 30-35.
[6]	YANG Sheng-bin, WU Ping, WANG Guo-ming. Stochastic enumerative algorithm optimization construction scheme of wastewater treatment station [J]. Journal of East China Normal University(Natural Sc, 2015, 2015(3): 21-30.
[7]	QI Lin-Ming, MIAO Lian-Ying, LI Wei-Qi. On the independence number of edge chromatic critical graphs [J]. Journal of East China Normal University(Natural Sc, 2015, 2015(1): 114-119.
[8]	CAI Gai-Xiang, YU Gui-Dong, XING Bao-Hua. Harary index of unicyclic graphs with n vertices and k pendent vertices [J]. Journal of East China Normal University(Natural Sc, 2015, 2015(1): 120-125.
[9]	WU Ya-Rong. On limit points of the third largest Laplacian eigenvalues of graphs [J]. Journal of East China Normal University(Natural Sc, 2015, 2015(1): 126-130.
[10]	LYU Chang-Qing . The linear arboricity of upper-embedded graph and secondary upper-embedded graph [J]. Journal of East China Normal University(Natural Sc, 2015, 2015(1): 131-135.
[11]	YU Jun, WEN Li-min. Bayes premium under variance-related principles with risk dependence [J]. Journal of East China Normal University(Natural Sc, 2014, 2014(4): 26-38.
[12]	LI Dan, WANG Guo-ping. On the spectral radius of weighted bicyclic graphs with a positive weight set [J]. Journal of East China Normal University(Natural Sc, 2014, 2014(4): 39-42.
[13]	REN Han, CHAO Fu-gang. Thomassen and coloring graphs on surfaces [J]. Journal of East China Normal University(Natural Sc, 2014, 2014(3): 1-7, 39.
[14]	ZHANG Xiao-jian, YANG Jia-shan. Oscillation and asymptotic behaviors for third-order delay dynamic equations on time scales [J]. Journal of East China Normal University(Natural Sc, 2014, 2014(3): 51-59.
[15]	DUAN Fang, ZHANG Wei-juan. On chromatic number of { 2K₁+K₂ , C₄}-free graphs [J]. Journal of East China Normal University(Natural Sc, 2014, 2014(1): 9-12.