Super Edge-Antimagic Total Labelings of \(M(K_{n,n,n})\)

Abstract

An \((a, d)\)-edge-antimagic total labeling on a \((p, q)\)-graph \(G\) is a one-to-one map \(f\) from \(V(G) \cup E(G)\) onto the integers \(1, 2, \ldots, p+q\) with the property that the edge-weights, \(w(uv) = f(u) + f(v) + f(uv)\) where \(uv \in E(G)\), form an arithmetic progression starting from \(a\) and having common difference \(d\). Such a labeling is called \emph{super} if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super \((a, d)\)-edge-antimagic total labeling of the disjoint union of multiple copies of the complete tripartite graph and the disjoint union of stars.