ON STRESS OF A VERTEX IN A GRAPH.

The stress of a vertex in a graph is the number of geodesics passing through it (A. Shimbel, 1953). A graph is k-stress regular if stress of each of its vertices is k. In this paper, we investigate some results and compute stress of vertices in some standard graphs and give a characterization of graphs with all vertices of zero stress except for one. Also we compute stress of vertices in graphs of diameter 2 and in the corona product Km 0G. Further we prove that any strongly regular graph is stress regular and characterize k-stress regular graphs for k = 0; 1; 2. [ABSTRACT FROM AUTHOR]