Odd and Even Distance Graphs

Let G = (V;E) be a (p; q) - graph. A shortest path P is called an odd path if l(P) is an odd positive integer. Odd distance graph OD(G) of a graph G is defined as the graph with vertex set V (G) and two vertices are adjacent if the distance between them is odd. 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.