A Unified Approach to Extremal Multiplicative Zagreb Indices for Trees, Unicyclic and Bicyclic Graphs

作者：Xu Kexiang; Hua Hongbo^*

来源：MATCH-Communications in Mathematical and in Computer Chemistry, 2012, 68(1): 241-256.

For a (molecular) graph, the (first or second) multiplicative Zagreb index Pi(1) or Pi(2) is a multiplicative variant of ordinary Zagreb index (M-1 or M-2). Gutman [6] determined that among all trees of order n >= 4, the extremal trees with respect to these multiplicative Zagreb indices are n-vertex path (with maximal Pi(1) and with minimal Pi(2)) and n-vertex star (with maximal Pi(2) and with minimal Pi(1)) Regarding these new topological indices, there is no further results reported so far. In this paper we investigate extremal properties of these indices along the same line of [8]. We first introduce some graph transformations which increase or decrease these two indices. As an application, we obtain a unified approach to characterize extremal (maximal and minimal) trees, unicyclic graphs and bicyclic graphs with respect to multiplicative Zagreb indices, respectively.

• 出版日期2012
• 单位淮阴工学院; 南京航空航天大学