路与广义Petersen图的直积图的Wiener指数

Wiener Index of the Direct Product of a Path and a Generalized Petersen Graph

图G和H的直积图G×H是一个顶点集为V(G)×V(H)的图,两点(g_(1),h_(1))和(g_(2),h_(2))是相邻的当且仅当g_(1)g_(2)是图G中的一条边,h_(1)h_(2)是图H中的一条边.连通图G的Wiener指数,记作W(G),是图G中无序点对之间的距离之和.最后得到了路与广义Petersen图P(m,3)的直积图的Wiener指数.

For two graphs G and H,the direct product G×H is the graph with vertex set V(G)×V(H)and two vertices(g_(1),h_(1))and(g_(2),h_(2))are adjacent whenever g_(1)g_(2) is an edge in G and h_(1)h_(2) is an edge in H.The Wiener index of a connected graph G,denoted by W(G),is the sum of the distances between all unordered pairs of vertices of G.In this paper,we obtain the Wiener index of the direct product of a path and a generalized Petersen graph P(m,3).