On acyclic and unicyclic conjugated graphs with maximum Zagreb indices

被引：0
作者：
Li, Shuchao [1 ]
Zhao, Qin [1 ]
机构：
[1] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China
来源：
UTILITAS MATHEMATICA | 2011年 / 86卷
基金：
美国国家科学基金会;
关键词：
Zagreb indices; Tree; Unicyclic graph; Perfect matching; m-matching; RANDIC INDEX; MOLECULAR-ORBITALS; 2ND-ZAGREB INDEX; TREES; BOUNDS; SQUARES; SUM;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a molecular graph, the first Zagreb index M-1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M-2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we first obtain a sharp upper bound on M-1-values of trees in terms of the order and the given size of matching. Then we investigate Zagreb indices of unicyclic conjugated graphs G (i.e., unicyclic graphs with a perfect matching) and a sharp upper bound on M-1(G), M-2(G) are determined, respectively. The sharp upper bounds for Zagreb indices of unicyclic graphs in terms of the order and given size of matching are also determined.
引用
收藏
页码：115 / 128
页数：14
相关论文
共 33 条
[1]  
[Anonymous], MATCH COMMUN COMPUT
[2]  
BALABAN AT, 1983, TOP CURR CHEM, V114, P21
[3]  
BONDY JA, 1976, GRAPH THEORY ITS APP
[4]  
Braun J, 2005, MATCH-COMMUN MATH CO, V54, P163
[5]   On the spectral radius of unicyclic graphs with perfect matchings [J].
Chang, A ;
Tian, F .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 370 :237-250
[6]   Extremal (n,n+1)-graphs with respected to zeroth- order general Randic index [J].
Chen, Shubo ;
Deng, Hanyuan .
JOURNAL OF MATHEMATICAL CHEMISTRY, 2007, 42 (03) :555-564
[7]   Sums of powers of the degrees of a graph [J].
Cioaba, Sebastian M. .
DISCRETE MATHEMATICS, 2006, 306 (16) :1959-1964
[8]  
Das KC, 2004, MATCH-COMMUN MATH CO, P103
[9]   Maximizing the sum of the squares of the degrees of a graph [J].
Das, KC .
DISCRETE MATHEMATICS, 2004, 285 (1-3) :57-66
[10]   An upper bound on the sum of squares of degrees in a graph [J].
de Caen, D .
DISCRETE MATHEMATICS, 1998, 185 (1-3) :245-248
1234