Odd and even Distance Graphs

Abstract

Let G = (V,E) be a (p, q) - graph. A shortest path P is called a odd path if l(P) is an odd positive integer . An odd distance graph OD(G) of graph G = (V,E) has the vertex set V = V (G) and two vertices in OD(G) are adjacent if they have an odd path in G. In this paper, we deal with the odd distance graph of standard graphs such as path, cycle, star, wheel, complete graph, complete bipartite graph and corona of a complete graph etc. Also we give some properties and characterizations for odd distance graphs.