Inertia and distance energy of line graphs of unicyclic graphs

被引:3
作者
Zhang, Xiaoling [1 ]
机构
[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Shandong, Peoples R China
关键词
Line graph; Distance spectral radius; Inertia; D-energy; SPECTRAL-RADIUS; MATRICES; TREES;
D O I
10.1016/j.dam.2018.06.023
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let D denote the distance matrix of a connected graph. The inertia of D is the triple of integers (n(+)(D), n(0)(D), n_(D)), where n(+)(D), n(0)(D), n_(D) denote the number of positive, 0, and negative eigenvalues of D, respectively. The D-energy is the sum of the absolute eigenvalues of D. In this paper, we first obtain the inertia and a formula for the determinant of the distance matrices of the line graphs of unicyclic graphs; Then, as applications, we obtain the graphs with maximum (resp. minimum) D-energy among all these graphs. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码:222 / 233
页数:12
相关论文
共 19 条
[1]   On the distance spectra of graphs [J].
Aalipour, Ghodratollah ;
Abiad, Aida ;
Berikkyzy, Zhanar ;
Cummings, Jay ;
De Silva, Jessica ;
Gao, Wei ;
Heysse, Kristin ;
Hogben, Leslie ;
Kenter, Franklin H. J. ;
Lin, Jephian C. -H. ;
Tait, Michael .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 497 :66-87
[2]  
[Anonymous], 1980, Spectra of graphs theory and application
[3]   COMPUTER-GENERATION OF DISTANCE POLYNOMIALS OF GRAPHS [J].
BALASUBRAMANIAN, K .
JOURNAL OF COMPUTATIONAL CHEMISTRY, 1990, 11 (07) :829-836
[4]   On distance matrices and Laplacians [J].
Bapat, R ;
Kirkland, SJ ;
Neumann, M .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 401 :193-209
[5]   Squared distance matrix of a tree: Inverse and inertia [J].
Bapat, R. B. ;
Sivasubramanian, Sivaramakrishnan .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 491 :328-342
[6]  
Consonni V, 2008, MATCH-COMMUN MATH CO, V60, P3
[7]  
Fan Y., 1994, DICT ALGEBRA
[8]  
Graham R. L., 1977, J GRAPH THEOR, V1, P85, DOI DOI 10.1002/JGT.3190010116
[9]   ADDRESSING PROBLEM FOR LOOP SWITCHING [J].
GRAHAM, RL ;
POLLAK, HO .
BELL SYSTEM TECHNICAL JOURNAL, 1971, 50 (08) :2495-+
[10]   Distance spectral radius of trees with given matching number [J].
Ilic, Aleksandar .
DISCRETE APPLIED MATHEMATICS, 2010, 158 (16) :1799-1806