Cordiality in the Context of Duplication in Helm and Closed Helm

Abstract

Let $G = (V(G) , E(G))$ be a graph and let $\displaystyle f:V(G)\rightarrow \{0,1\}$ be a mapping from the set of vertices to \{0,1\} and for each edge $uv \in E$ assign the label $|f(u)-f(v)|$. If the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labled with 0 and the number of edges labeled with 1 differ by at most 1, then $f$ is called a cordial labeling. We discuss cordial labeling of graphs obtained from duplication of certain graph elements in helm and closed helm.