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All Journal Indonesian Journal of Combinatorics
Earl Baron Marzan Almanzor
University of the Philippines Los Baños
Computer Science & IT Decision Sciences, Operations Research & Management

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Totally antimagic total labeling of helm and gear graphs Earl Baron Marzan Almanzor; Michael Kirby Briones Rodriguez
Indonesian Journal of Combinatorics Vol 10, No 1 (2026)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2026.10.1.3

Abstract

A total labeling of a graph G is a bijection from the union of the vertex set and the edge set of G to the set {1,2,...,|V(G)|+|E(G)|}. Under a total labeling, the vertex-weight of a vertex is defined as the sum of its label and the labels of all edges incident to it. Similarly, the edge-weight of an edge is the sum of its label and the labels of its two end vertices. A total labeling is said to be edge-antimagic total if all the edge-weights are pairwise distinct, and vertex-antimagic total if all the vertex-weights are pairwise distinct. If a total labeling is edge-antimagic total and vertex-antimagic total at the same time, then it is called a totally antimagic total labeling. A graph that admits totally antimagic total labeling is called a totally antimagic total graph. In this paper, we show that helm graphs Hn and gear graphs Gn are totally antimagic total graphs.
Co-Authors Michael Kirby Briones Rodriguez