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.

Chelo Index for Graphs

“…The Wiener index W (G) of a connected graph G is defined to be the sum of distances between all vertex pairs in G. The Wiener index is substantially used in theoretical chemistry for the design of quantitative structure-property relations (mainly with physico-chemical properties) and quantitative structure-activity relations including biological activities of the respective chemical compounds. For new topological indices, we suggest the reader to refer the papers [7], [9][10][11][12]. Rajendra et al [13] have recently introduced the concept of peripheral geodesic index.…”