MMD labeling in the context of larger families of bipartite graphs

Abstract

Let the graph G has r vertices and let g be a relation from the vertex set of G to {1,2,…,r} such 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 the edge set of 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 discuss an arbitrary super subdivision of MMD bipartite graphs.