路与圈的笛卡尔积的Wiener指数

The Wiener Index of Cartesian Product Graphs of Paths and Cycles

设G=(V,E)是一个简单无向图,图G的Wiener指数W(G)是指G中所有顶点对之间的距离之和,它是图论中一类重要的研究内容。利用路的Wiener指数的对称性,将路P_(n)与路P_(m)的笛卡尔积和路P_(m)与圈C_(n)的笛卡尔积进行分块,通过求和得到了P_(n)×P_(m)和C_(n)×P_(m)的Wiener指数。

Let G=(V,E)be a simple undirected graph,the Wiener index W(G)of a graph G is the sum of distances between all pairs of vertices of G.It is an important class of research content in graph theory.This paper takes advantage of the symmetry of the Wiener index of the path,divide the Cartesian product of path P_(n) and path P_(m) and the Cartesian product of path P_(m) and cycle C_(n),the Wiener index of P_(n)×P_(m) and C_(n)×P_(m) are obtained by adding them together.