k-Zumkeller Labeling for Twig Graphs

Let G=(V,E) be a graph. An injective function f:V→N is said to be a k-Zumkeller labeling of the graph G if the induced function f⁎:E→N defined by f⁎(xy)=f(x)f(y) satisfies the following conditions(i)For every xy∈E, f⁎(xy) is a Zumkeller number.(ii)|f⁎(E)|=k, where |f⁎(E)| denotes the number of distinct Zumkeller numbers on the edges of the graph G. In this paper we prove that twig graphs admit a 4-Zumkeller labeling.