The graceful labeling of Vee graphs

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematics and Natural Science, University of Mataram, Mataram, Indonesia

2 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Gadjah Mada, ogyakarta, Indonesia

3 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, Indonesia

10.22108/toc.2025.143231.2220

Abstract

Graph labeling is the process of assigning numerical values, typically integers, to the elements of a graph. This study focuses on a specific type of labeling called graceful labeling. In graceful labeling, each vertex of the graph is assigned a unique number such that the differences between these numbers assigned to the end vertices of each edge result in unique values. This article introduces a new graph structure called the Vee graph, which is formed by attaching two grid graphs at one of their corresponding end edges. We demonstrate that the Vee graph can be labeled gracefully, meaning that it satisfies the criteria of graceful labeling. Additionally, the paper provides examples to illustrate graceful labeling for different variations of Vee graphs.

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References

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Transactions on Combinatorics
Volume 15, Issue 3 - Serial Number 3
September 2026
Pages 159-170

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History

  • Receive Date: 01 November 2024
  • Revise Date: 22 June 2025
  • Accept Date: 25 June 2025
  • Published Online: 05 August 2025

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