On difference of Zagreb indices

被引：117
作者：
Furtula, Boris [1 ]
Gutman, Ivan [1 ]
Ediz, Suleyman [2 ]
机构：
[1] Univ Kragujevac, Fac Sci, Kragujevac, Serbia
[2] Yuzuncu Yil Univ, Fac Educ, TR-65080 Van, Turkey
来源：
DISCRETE APPLIED MATHEMATICS | 2014年 / 178卷
关键词：
Degree (of vertex); Zagreb index; First Zagreb index; Second Zagreb index; SQUARES; SUM; IRREGULARITY;
D O I：
10.1016/j.dam.2014.06.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The classical first and second Zagreb indices of a graph G are defined as M-1 = Sigma(v) d(v)(2) and M-2 = Sigma(uv) d(u) d(v), where d(v) is the degree of the vertex v of G. So far, the difference of M-1 and M-2 has not been studied. We show that this difference is closely related to the vertex-degree-based invariant RM2 = Sigma(uv) (d(u) - 1) (d(v) - 1), and determine a few basic properties of RM2. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：83 / 88
页数：6
相关论文
共 34 条
[1]   On the Zagreb indices equality [J].
Abdo, Hosam ;
Dimitrov, Darko ;
Gutman, Ivan .
DISCRETE APPLIED MATHEMATICS, 2012, 160 (1-2) :1-8
[2]  
Andova V, 2011, MATCH-COMMUN MATH CO, V65, P647
[3]   On the Zagreb index inequality of graphs with prescribed vertex degrees [J].
Andova, Vesna ;
Bogoev, Saso ;
Dimitrov, Darko ;
Pilipczuk, Marcin ;
Skrekovski, Riste .
DISCRETE APPLIED MATHEMATICS, 2011, 159 (08) :852-858
[4]  
BALABAN AT, 1983, TOP CURR CHEM, V114, P21
[5]   A NOTE ON THE IRREGULARITY OF GRAPHS [J].
BELL, FK .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 161 :45-54
[6]  
Bogoev S, 2011, MATCH-COMMUN MATH CO, V66, P647
[7]   Variable neighborhood search for extremal graphs: 1 The AutoGraphiX system [J].
Caporossi, G ;
Hansen, P .
DISCRETE MATHEMATICS, 2000, 212 (1-2) :29-44
[8]  
Caporossi G, 2010, MATCH-COMMUN MATH CO, V63, P441
[9]   Sums of powers of the degrees of a graph [J].
Cioaba, Sebastian M. .
DISCRETE MATHEMATICS, 2006, 306 (16) :1959-1964
[10]  
Das K. C., 2003, Kragujevac J. Math, V25, P19
1234