S - magic Labelings of Union of Disjoint Complete Multipartite Graphs - Wichianpaisarn, Tanawat; Mato, Uthoomporn (Burapha Science Journal, 2026)
An magic labeling of a graph is a one to one map from the vertex set to a set of positive integers with , such that for any where is a constant and is the set of vertices in adjacent to . A graph is magic if admits an magic labeling. In this paper, we show a necessary and sufficient condition for the existence of an magic labelings of a union of disjoint complete multipartite graphs , we also prove that the graph adding one edge is not magic if two endpoints of are from the same partite set.