On Divisor 3-Equitable Labeling of Wheel Graphs

Abstract

A graph on vertices is said to admit a divisor 3-equitable labeling if there exists a bijection defined by and for all , where denotes the number of edges labelled with . A graph which permits a divisor 3-equitable labeling is called a divisor 3-equitable graph. A wheel graph is defined as , where is a cycle on vertices and is a complete graph on a single vertex. In this paper, we prove the non-existence of a divisor 3-equitable labeling of the wheel graph for .