Proximity Prestige of a Vertex in Some Graph Families

Let G = (V, E) be an undirected graph where V and E are the set of vertices and edges respectively. The proximity prestige (P P) of a vertex vi is the sum of the shortest path distance between vertex i and j all over the number of vertices in the graph. Proximity prestige (P P) emphasizes the importance of both reachability and distance. Here, general properties of proximity prestige in some graph classes, including path, cycle, complete, friendship, complete bipartite, star, fan and wheel were determined.