MMD labeling of some graph families

Abstract

Let the graph G has r vertices and let g be a relation from V(G) to {1,2,…,r} so that each vertex takes exactly one value i, 1 ≤ i ≤ r which is both one to one and onto. Let g* be a function induces edge labeling from E(G) to {0,1,…r-1}defined as g*(wv)=g(w)g(v)(mod r), for every edge vw in G. Collecting all edge labels and finding their addition if it is the divisor of r then the graph G is a modular multiplicative divisor (MMD) graph. Here constructed larger families of MMD graph and discuss MMD labeling of join of two graphs, one of the graph operations and complete tripartite MMD graphs. Discuss related open problems.