Super Edge-Magic Total Labelings of ?? × ?? With ?? Pendants - Rica Amalia; Kholifatur Rohmah; Khairil Anam (Contemporary Mathematics and Applications (ConMathA), 2026)
A graph ? is defined as a finite nonempty set ? of objects called vertices (vertex for singular) together with a possibly empty set of ? ⊆ {{?, ?} ∣ ?, ? ∈ ?} called edges. One of interesting topic in graph theory is graph labelling. Super edge magic total labeling is a special form of total edge magic labeling, where vertex labels must come from the set {1,2,…,|?|}, while edge labels come from the remainder of the set {1,2,…,|?|+|?|}. Formally, this labeling is a bijective mapping: ? : ? ∪ ?→{1,2,…,|?|+|?|} with the following conditions: ?(?) ∈ {1,2,...,|?|} ∀? ∈ ? where there is a constant number ? such that for every edge ? = ?? ∈ ?, ?(?) + ?(?) + ?(?) = ?. The main focus of this research is to determine the existence and construction of super edge-magic total labeling on cartesian product graph ?? × ?? with additional pendants. In this study, we get that ?? × ?? with pendants are graphs with super edge-magic total labelling’s by constructing the labeling of their vertices and edges, thereby obtaining a magic constant ?.