Indonesian Journal of Combinatorics
Vol 10, No 1 (2026)

Totally antimagic total labeling of helm and gear graphs

Earl Baron Marzan Almanzor (University of the Philippines Los Baños)
Michael Kirby Briones Rodriguez (University of the Philippines Los Baños)



Article Info

Publish Date
29 Jun 2026

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.

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Journal Info

Abbrev

ijc

Publisher

Subject

Computer Science & IT Decision Sciences, Operations Research & Management

Description

Indonesian Journal of Combinatorics (IJC) publishes current research articles in any area of combinatorics and graph theory such as graph labelings, optimal network problems, metric dimension, graph coloring, rainbow connection and other related topics. IJC is published by the Indonesian ...