On the Existence of Cn-Supermagic Labelings in Cycle-Based Graph Structures

Year 2025, Volume: 14 Issue: 2, 82 - 99, 31.08.2025

Tarkan Öner

https://doi.org/10.54187/jnrs.1646665

Abstract

In this paper, we prove the existence of Cn-supermagic labeling for the graph G(n, n) formed by connecting a vertex of n copies of the Cn (n-edge cycle) graph to a vertex of a main Cn graph. Labeling functions enable the edges and the vertices of the graph to be labeled with subgraphs that resemble the structure of Cn. Cn-supermagic labeling requires the sum of the labels to be constant for each Cn-cover, and the labels must be uniquely distributed across the graph. The study examines different labelings of G(n, n) based on the value of n modulo 4, demonstrating their validity through examples. The results show that such labelings are possible and can be applied consistently for specific values of n.

Keywords

Graph labeling , Cn-supermagic labeling , circular graph , magic sum , H-cover

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