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  be a graph. A one-one function  is called a t-m-Zumkeller labeling of the graph G if the induced function  defined by  satisfies the following conditions:

1. For every  is an m-Zumkeller number.
2. where t denotes the number of distinct m-Zumkeller numbers on the edges of G.

If a graph  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.

m-Zumkeller numbers, t-m-Zumkeller labeling, comb graphs, ladder graphs, twig graphs.