Abstract
A k-Zumkeller labeling for the graph G = (V, E) is an assignment f of a label to each vertices of G such that each edge uv is an element of E is assigned the label f (u) f (v), the resulting edge labels are k distinct Zumkeller numbers. In this paper, we prove that the graph P-m x P-n is k-Zumkeller graph for m, n >= 3 while P-m x C-n and C-m x C-n are k-Zumkeller graphs for n = 4 (mod2). Also we show that the graphs P-m circle times P-n and P-m circle times C-n for m, n >= 3 admit k-Zumkeller labeling. Further, the graph C-m circle times C-n where m or n is even admit a k-Zumkeller labeling.