Geometric Mean Cordial Labeling of Helm Graph

Abstract

Let  be a graph with vertex set  and edge set . Let  be a mapping. Assign the label  is called a geometric mean cordial (GMC) labeling if  and , where the number of vertices and edges labeled with  is denoted by and  respectively. A graph with a GMC labeling is called a GMC graph. In this research article we investigate the GMC labeling of Helm graph  and also establish the GMC labeling of some graph operations on Helm graph such as Fusion and Duplication. We also prove that the graph operation Switching on Helm graph does not admit GMC labeling.