Characterization of certain families of modular multiplicative divisor graphs. Issue 2 (1st March 2017) - Revathi, R.; Ganesh, S.
Abstract: A modular multiplicative divisor (MMD) labelling of a graph G with p vertices and q edges is a bijection f from the set of all vertices to the set of positive integers {1, 2,  …,   p } such that the sum of all edge labels f* ( uv ) =  f ( u ) f ( v )( modp ); uv  ∈  E ( G ) is a multiple of p . In this paper, we characterize certain classes of MMD graphs. This result is a solution to the open problem posed by G. Sethuraman in AKCE International Journal of Graphs and Combinatorics, No. 1 (2009) 229–236. In addition, we discuss the role of MMD labelling in obtaining cyclic decompositions of certain families of graphs into specific graphs.