k-Zumkeller Graphs through Splitting of Graphs





Zumkeller number, k-Zumkeller graph, splitting graph


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:

  1. f (xy) is a Zumkeller number for every xy ∈ E.
  2. 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.

Author Biographies

M. Kalaimathi , Vellore Institute of Technology.

Division of Mathematics, School of Advanced Sciences.

B. J. Balamurugan, Vellore Institute of Technology.

Division of Mathematics, School of Advanced Sciences.


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How to Cite

M. Kalaimathi and B. J. Balamurugan, “k-Zumkeller Graphs through Splitting of Graphs”, Proyecciones (Antofagasta, On line), vol. 42, no. 3, pp. 775-794, May 2023.




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