New Constructions of Super Edge Bimagic Labeling

Abstract

A graph $G(p,q)$ is said to be total edge bimagic with two common edge counts $k_1$ and $k_2$ if there exists a bijection $f:V(G)\cup E(G)\to \{1,2,\dots ,p+q\}$ such that for each edge $uv\in E(G)$, $f(u)+f(v)+f(uv)=k_1$ or $k_2$.
A total edge-bimagic graph is called super edge-bimagic if $f(V(G))=\{1,2,\dots ,p\}$. In this paper, we define new types of super edge-bimagic labeling and prove some interesting results related to super edge-bimagic labeling. Also, its relationship with cordial labeling is studied.