RICHNESS OF A VERTEX IN A GRAPH

Abstract

The stress of a vertex in a graph is the number of geodesics passing through it. The status of a vertex $v$ in a graph is the sum of the distances from $v$ to all other vertices. We define the richness of a vertex $v$ in a graph as the status of $v$ minus the stress of $v$. The total richness of a graph is the sum of richness of all the vertices in that graph. We made some observations, compute richness of vertices in some standard graphs and obtain some interesting results.