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All Journal Contemporary Mathematics and Applications (ConMathA) JURNAL AKSIOMA AL-ASAS Indonesian Journal of English Teaching
Kholifatur Rohmah
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Religion Education Languange, Linguistic, Communication & Media Materials Science & Nanotechnology Mathematics Social Sciences Other

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Journal : Contemporary Mathematics and Applications (ConMathA)

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Super Edge-Magic Total Labelings of ?? × ?? With ?? Pendants Rica Amalia; Kholifatur Rohmah; Khairil Anam
Contemporary Mathematics and Applications (ConMathA) Vol. 8 No. 1 (2026)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v8i1.85975

Abstract

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 ?.
Co-Authors Dea Ramadhani Ive Emaliana Khairil Anam Latifatun Nabila Nurul Ismaiyah Rica Amalia Zainah