On modular multiplicative divisor graphs

Abstract

A graph G (V, E) with /V/ = n is said to have Modular Multiplicative Divisor (MMD) labeling if there exist a bijection f: V(G)→{1, 2, n} 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. In this paper we prove that the split graph of cycle C_n, helm graph H_n, flower graph f_nX4, cycle cactus C₄ (n) and extended triplicate graph of a path P_n (ETG(P_n)) admits Modular Multiplicative Divisor labeling. AMS Subject Classification: 05C78