On Randic energy

被引：103

作者：

Gutman, Ivan ^{[1
,2
]}

Furtula, Boris ^{[1
]}

Bozkurt, S. Burcu ^{[3
]}

机构：

[1] Univ Kragujevac, Fac Sci, Kragujevac 34000, Serbia

[2] King Abdulaziz Univ, Fac Sci, Dept Chem, Jeddah 21589, Saudi Arabia

[3] Selcuk Univ, Fac Sci, Dept Math, TR-42075 Konya, Turkey

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 442卷

关键词：

Graph spectrum; Graph energy; Randic matrix; Randic energy; Normalized Laplacian matrix; Normalized signless Laplacian matrix; Normalized Laplacian energy; SIGNLESS LAPLACIAN; SPECTRAL THEORY; INDEX; GRAPHS; NARUMI; MATRIX;

D O I：

10.1016/j.laa.2013.06.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Randic matrix R = (r(ij)) of a graph G whose vertex vi has degree d(i) is defined by r(ij) = 1/root d(i)d(j) if the vertices v(i) and v(j) are adjacent and r(ij) = 0 otherwise. The Randic. energy RE is the sum of absolute values of the eigenvalues of R. RE coincides with the normalized Laplacian energy and the normalized signless-Laplacian energy. Several properties or R and RE are determined, including characterization of graphs with minimal RE. The structure of the graphs with maximal RE is conjectured. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：50 / 57

页数：8

共 36 条

[1]

Bozkurt SB, 2012, EUR J PURE APPL MATH, V5, P88

[2]

Bozkurt SB, 2010, MATCH-COMMUN MATH CO, V64, P321

[3]

Bozkurt SB, 2010, MATCH-COMMUN MATH CO, V64, P239

[4] 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

[5]

Chung F., 1992, Spectral Graph Theory

[6]

Coulson CA, 1940, P CAMB PHILOS SOC, V36, P201

[7]

Cvetkovi DM., 1980, Spectra of Graphs: Theory and Applications

[8] Signless Laplacians of finite graphs [J].

Cvetkovic, Dragos ;

Rowlinson, Peter ;

Simic, Slobodan K. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 423 (01) :155-171

[9] TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, III [J].

Cvetkovic, Dragos ;

Simic, Slobodan K. .

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2010, 4 (01) :156-166

[10] TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, I [J].

Cvetkovic, Dragos ;

Simic, Slobodan K. .

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2009, 85 (99) :19-33

← 1 2 3 4 →