Diametral paths in extended transformation graphs

Abstract

In a graph, diametral path is shortest path between two vertices which has length equal to diameter of the graph. Number of diametral paths plays an important role in computer science and civil engineering. In this paper, we introduce the concept of extended transformation graphs. There are 64 extended transformation graphs. We obtain number of diametral paths in some of the extended transformation graphs and we also study the semi-complete property of these extended transformation graphs. Further, a program is given for obtaining number of diametral paths.