On Divisor 3-Equitable Labeling of Wheel Graphs

A graph on vertices is said to admit a divisor 3- equitable labeling if there exists a bijection ∶ () → {, , . . . , } defined by = = ,()| or |() , = = , 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 ≥ .