Indian Journal of Science and Technology

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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
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