On the Zagreb matrix and Zagreb energy

被引：3

作者：

Jahanbani, Akbar ^{[1
]}

Khoeilar, Rana ^{[1
]}

Shooshtari, Hajar ^{[1
]}

机构：

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

来源：

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS | 2022年 / 15卷 / 01期

关键词：

Eigenvalues of matrix; spread of matrix; Zagreb energy; first Zagreb index; LOWER BOUNDS; ESTRADA INDEX;

D O I：

10.1142/S179355712250019X

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 du be the degree of vertex u in a graph G. The Zagreb matrix of G is the square matrix of order n whose (i,j)-entry is equal to d(u) + d(v) if the vertex u and the vertex v of G are adjacent, and 0 otherwise. This matrix, related closely to the Zagreb (abbreviated as Z) index. The Zagreb eigenvalues of G are the eigenvalues of its Z matrix and the Zagreb energy of G is the sum of the absolute values of its Zagreb eigenvalues. In this paper, we obtain some new results for the eigenvalues of the Zagreb matrix, the spread of the Zagreb matrix. Moreover, we obtain some new bounds for the Zagreb energy of a graph.

引用

页数：15

共 31 条

[11] On Randic energy [J].

Gutman, Ivan ;

Furtula, Boris ;

Bozkurt, S. Burcu .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 442 :50-57

[12]

Jahanbani A, 2020, MATCH-COMMUN MATH CO, V83, P497

[13]

Jahanbani A, 2019, COMPUT SCI J MOLD, V27, P188

[14] Lower bounds for the energy of graphs [J].

Jahanbani, Akbar .

AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2018, 15 (01) :88-96

[15]

Jahanbani A, 2018, MATCH-COMMUN MATH CO, V79, P275

[16] Some new lower bounds for energy of graphs [J].

Jahanbani, Akbar .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 296 :233-238

[17] General Randic matrix and general Randic incidence matrix [J].

Liu, Ruifang ;

Shiu, Wai Chee .

DISCRETE APPLIED MATHEMATICS, 2015, 186 :168-175

[18]

Lupas A., 1977, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Math. Fiz., V577/598, P79

[19] Characterizations and lower bounds for the spread of a normal matrix [J].

Merikoski, JK ;

Kumar, R .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 364 :13-31

[20] Remark on spectral study of the geometric-arithmetic index and some generalizations [J].

Milovanovic, E. I. ;

Milovanovic, I. Z. ;

Matejic, M. M. .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 334 :206-213

← 1 2 3 4 →