平方图的顶点PI指数

The vertex PI index of power graphs

设G=(V,E)为简单连通图,称PI_(v)(G)=∑_(e=uv∈E)(n_(u)(e|G)+n_(v)(e|G))为G的顶点PI指数,其中n_(u)(e|G)表示图G中到边e=uv的端点u的距离小于到端点v的距离的顶点数,n_(v)(e|G)表示图G中到边e=uv的端点v的距离小于到端点u的距离的顶点数.用分类讨论法得到了圈和路的平方图的顶点PI指数.

LetG=(V,E)be a simple graph and the vertex PIindex of graph G is defined as PI_(v)(G)=Σ_(e=uv∈E)(n_(u)(e|G)+n_(v)(e|G)),where n_(u)(e|G)denotes the number of vertices of G whose distance to the vertex u is smaller than the distance to the vertex v,and n_(v)(e|G)denotes the number of vertices of G whose distance to the vertex v is smaller than the distance to the vertex u.In this paper,we obtain the vertex PI index of Power graph of Cycle and Path by uses the classification discussion method.