Indian Journal of Science and Technology

Abstract

A graph G (V, E) with |V| = n is said to have modular multiplicative divisor labeling if there exist a bijection f: V(G) → {1, 2, …,} and the induced function f*: E(G) → {0, 1, 2, …, n – 1} where f*(uv) = f(u)f(v) (mod n) such that n divides the sum of all edge labels of G. We prove that the path Pn , and the graph Pa, b (a graph which connects two vertices by means of “b” internally disjoint paths of length “a” each), shadow graph of a path and the cartesian product Pn × P1 , (n is not a multiple of 6) admits modular multiplicative divisor labeling. Also we discuss the upper bound for the number of edges in a modular multiplicative divisor graphs.

AMS Subject Classification: 05C78

Keywords: Graph Labeling, Path, Graph Pa, b, Shadow Graph D2 (G), The Cartesian Product Pn × P1