Product cordial graph in the context of some graph operations on crown, helm, and wheel graph

A graph labeling is an assignment of integers to the vertices or edges or both subject to some conditions. The concept of cordial labeling was introduced by Ibrahim Cahit in 1987 as a weaker version of graceful and harmonious labeling. A product cordial labeling of a graph 𝐺 = (𝑉(𝐺), 𝐸(𝐺)) is a function 𝑓: 𝑉(𝐺) → {0,1} with each edge 𝑢𝑣 assign label 𝑓(𝑢)𝑓(𝑣) , such that the number of vertices with label 0 and the number of vertices with label 1 differ at most by 1, and the number of edges with label 0 and the number of edges with label 1 differ by at most 1. In this paper we investigate product cordial labeling of the graphs obtained by duplication of some graph elements in crown, helm and wheel graph.