On the inverse sum indeg energy of trees

被引：0

作者：

Hatefi, H. ^{[1
]}

Ahangar, H. Abdollahzadeh ^{[2
]}

Khoeilar, R. ^{[1
]}

Sheikholeslami, S. M. ^{[1
]}

机构：

[1] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran

[2] Babol Noshirvani Univ Technol, Dept Math, Shariati Ave, Babol 4714871167, Iran

来源：

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2022年 / 15卷 / 09期

关键词：

Tree; inverse sum indeg index; inverse sum indeg energy; LOWER BOUNDS; MATRIX;

D O I：

10.1142/S1793557122501765

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a graph of order n and d(i) be the degree of the vertex v(i), for i = 1, 2, ..., n. The ISI matrix of G is the square matrix of order n whose (i, j)-entry is equal to d(i)d(j)/d(i)+d(j) if v(i) is adjacent to v(j), and zero otherwise. Let mu(1) > mu(2) > ... > mu(n), be the eigenvalues of ISI matrix. The ISI energy of a graph G, denoted by xi(ISI)(G), is defined as the sum of the absolute values of the eigenvalues of ISI matrix. In this paper, we prove that the star has the minimum ISI energy among trees.

引用

页数：19

共 35 条

[1] The energy of a graph [J].

Balakrishnan, R .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 387 :287-295

[2] On the normalized Laplacian energy and general Randic index R_1 of graphs [J].

Cavers, Michael ;

Fallat, Shaun ;

Kirkland, Steve .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 433 (01) :172-190

[3] Degree-based energies of graphs [J].

Das, Kinkar Ch ;

Gutman, Ivan ;

Milovanovic, Igor ;

Milovanovic, Emina ;

Furtula, Boris .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 554 :185-204

[4] On spectral radius and energy of extended adjacency matrix of graphs [J].

Das, Kinkar Ch. ;

Gutman, Ivan ;

Furtula, Boris .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 296 :116-123

[5] The ABC Matrix [J].

Estrada, Ernesto .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2017, 55 (04) :1021-1033

[6] The minimum ABC energy of trees [J].

Gao, Yubin ;

Shao, Yanling .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 577 :186-203

[7] ACYCLIC SYSTEMS WITH EXTREMAL HUCKEL PI-ELECTRON ENERGY [J].

GUTMAN, I .

THEORETICA CHIMICA ACTA, 1977, 45 (02) :79-87

[8]

Gutman I, 2001, ALGEBRAIC COMBINATORICS AND APPLICATIONS, P196

[9]

Gutman I., 2012, Mathematical concepts in organic chemistry

[10]

Gutman I., 1986, MATH CONCEPTS ORGANI

← 1 2 3 4 →