Wiener index of a type of composite graph

作者：Hu Mingjun^*

来源：Ars Combinatoria, 2012, 106: 59-64.

• Distance in graphs
• Wiener index
• double graph
• extremal graphs

Wiener index, one of the oldest molecular topological descriptors used in mathematical chemistry, was well-studied during the past decades. For a graph G, its Wiener index is defined as W(G) = Sigma({u,) (v}subset of V(G)) d(G)(u, v), where d(G)(u, v) is the distance between two tices u and v in G. In this paper, we study Wiener index of a class of composite graph, namely, double graph. We reveal the relation between the Wiener index of a given graph and the one of its double graph as well as the relation between Wiener index of a given graph and the one of its k-iterated double graph. As a consequence, we determine the graphs with the maximum and minimum Wiener index among all double graphs and k-iterated double graphs of connected graphs of same order, respectively.

• 出版日期2012-7
• 单位安徽建筑大学