On super edge-magic total labeling of certain classes of graphs

Muhammad Imran, Mehar Ali Malik, Muhmmad Yasir Hayat Malik

Abstract


A $(p, q)$- simple graph is edge-magic if there exists a bijective function $\lambda:V(G)\cup E(G)\rightarrow \{1, 2, \dots, p+q\}$ such that $\lambda(u)+\lambda(uv)+\lambda(v)=k$, for all edge $uv\in E(G),$ where $k$ is called the magic constant or sometimes the valence of $\lambda$. An edge-magic total labeling $\lambda$ is called super edge-magic total if $\lambda(V(G))=\{1, 2, \dots, p\}$. In this paper, we construct new classes of trees using w- trees and generalized combs and prove that they admit super edge magic total labeling. We also prove that the extended umbrella graphs admit super edge-magic total labeling.

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