k-Zumkeller Graphs through Splitting of Graphs
DOI:
https://doi.org/10.22199/issn.0717-6279-5723Keywords:
Zumkeller number, k-Zumkeller graph, splitting graphAbstract
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.
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