(1, N)-arithmetic graphs. Issue 1 (2nd January 2016) - Ramachandran, V.; Sekar, C.
Abstract : A ( p, q )-graph G is said to be (1, N )-arithmetic if there is a function from the vertex set V ( G ) to so that the values obtained as the sums of the labeling assigned to their end vertices, can be arranged in the arithmetic progression . In this paper, we prove that Stars, Paths, complete bipartite graph, highly irregular graph and Cycle are (1, N )-arithmetic, is not (1, N )-arithmetic. We also prove that no graph G containing an odd cycle is (1, N )-arithmetic for every positive integer N .