Sharp bounds on Zagreb indices of cacti with k pendant vertices

被引：38
|
作者：
Li, Shuchao [1 ]
Yang, Huangxu [1 ]
Zhao, Qin [1 ]
机构：
[1] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China
来源：
FILOMAT | 2012年 / 26卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Zagreb indices; Cactus graphs; Pendant vertex; CONNECTIVITY INDEX; GRAPH-THEORY; MOLECULAR CONNECTIVITY; TOPOLOGICAL INDEXES; 2ND-ZAGREB INDEX; UNIFIED APPROACH; RANDIC INDEX; TREES; ORBITALS; MAXIMUM;
D O I：
10.2298/FIL1206189L
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 its vertex degrees, and the second Zagreb index M-2 is equal to the sum of products of degrees of pairs of adjacent vertices. A connected graph G is a cactus if any two of its cycles have at most one common vertex. In this paper, we investigate the first and the second Zagreb indices of cacti with k pendant vertices. We determine sharp bounds for M-1-, M-2-values of n-vertex cacti with k pendant vertices. As a consequence, we determine the n-vertex cacti with maximal Zagreb indices and we also determine the cactus with a perfect matching having maximal Zagreb indices.
引用
收藏
页码：1189 / 1200
页数：12
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