On Super Magic Algorithm for Union of Comb and Star Graph

Abstract

In [7], Enomoto \emph{et al.} identified the concept of super edge magic total labeling of graphs by getting motivation from the idea of edge-magic labeling of graphs that was brought into light by Kotzig and Rosa [20]. An edge magic total labeling of a graph $G$ is a one to one map $\phi$ from $V(G)\cup E(G)$ onto the set $ \{1, 2, \dots , |V(G)|+|E(G)|\}$ with the property that, there is an integer constant $\alpha$ such that $\phi(u)+\phi(uv)+\phi(v)=\alpha$ for any $(u,v)\in E(G).$ Moreover if $\phi(V(G))=\{1, 2, \dots , |V(G)|\}$, then edge magic total labeling is called super edge magic total labeling. In this paper, we study the super edge magic total labeling of generalized comb graph.