Let G = (V,E) be a simple graph with vertex set V and edges set E.  A 1−1 function f : V → N is said to induce a k-Zumkeller graph G if the induced edge function f ∗ : E → N defined by f ∗(xy) = f(x)f(y) satisfies the following conditions: f ∗(xy) is a Zumkeller number for every xy ∈ E. The total distinct Zumkeller numbers on the edges of G is k. In this article, we compute k-Zumkeller graphs through the graph splitting operation on path, cycle and star graphs.