New Constructions of Super Edge Bimagic Labeling

A graph \( G(p, q) \) is said to be \textit{total edge bimagic} with two common edge counts \( k_1 \) and \( k_2 \) if there exists a bijection \( f: V(G) \cup E(G) \to \{1, 2, \ldots, p + q\} \) 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 \textit{super edge-bimagic} if \( f(V(G)) = \{1, 2, \ldots, p\} \). 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.