t-m-ZUMKELLER LABELING OF GRAPHS

A positive integer n is called an m-Zumkeller number if the set of all the positive divisors of n can be partitioned into two disjoint subsets of equal product. Let G = (V, E) be a graph. A one-one function f : V -> N is called a t-m-Zumkeller labeling of the graph G if the induced function f* : E -> N defined by f*(uv) = f(u) f(v) satisfies the following conditions: i. For every uv is an element of E, f*(uv) is an m-Zumkeller number. ii. vertical bar f*(E)vertical bar = t, where t denotes the number of distinct m-Zumkeller numbers on the edges of G. If a graph G = (V, E) admits a t-m-Zumkeller labeling, then the graph is known as t-m-Zumkeller graph. In this paper, we prove the existence of t-m-Zumkeller labeling of different types of graphs viz., (i) paths, (ii) cycles, (iii) comb graphs, (iv) ladder graphs and (v) twig graphs.