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 KmββG. Further we
prove that any strongly regular graph is stress regular and characterize
k-stress regular graphs for k=0,1,2.Comment: 11 pages, 12 figures, accepted for publication in Palestine Journal
of Mathematic