Zumkeller labeling of some path related graphs

Abstract

A positive integer n is said to be Zumkeller number if its positive factors can be partitioned into 2 disjoint parts with the equal sum, that is each part with sum σ (n)/2. Let G = (V (G), E(G)) be a graph. An one to one function f defined on V (G) to a subset of natural numbers is termed as Zumkeller labeling of G if the induced function) admits Zumkeller labeling is called a Zumkeller graph. In this manuscript, we investigate Zumkeller labeling for several classes of path graph.