The Modular Chromatic Number of The Corona Product of a Generalized Jahangir Graph

P Sumathi; S Tamilselvi

doi:10.17485/IJST/v16i46.2028

Article

The Modular Chromatic Number of The Corona Product of a Generalized Jahangir Graph

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i46.2028

Year: 2023, Volume: 16, Issue: 46, Pages: 4309-4327

Original Article

The Modular Chromatic Number of The Corona Product of a Generalized Jahangir Graph

P Sumathi¹, S Tamilselvi^2*

¹Associate Professor, Department of Mathematics, C. Kandaswami Naidu College for Men, Anna Nagar, 600 102, Chennai, India
²Assistant Professor, Department of Mathematics, School of Arts And Science, AV Campus, Chennai, India

*Corresponding Author
Email: [email protected]

Received Date:17 October 2022, Accepted Date:13 October 2023, Published Date:13 December 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The objective of this study is to investigate modular coloring for product graphs such as the corona product of the family of Jahangir graphs. This paper minimizes the number of colors assigned to the vertex of the graph to achieve the modular chromatic number of . Methods: The modular k-coloring of a graph is an injective map , where the color sum is different for adjacent vertices of ; that is, , for . The modular chromatic number of G is the minimum for which has a modular -coloring. Findings: In this paper, we verified the minimum k for which the corona product of a generalized Jahangir graph admits modular k-coloring and determined the modular chromatic number of for all integers . Novelty: This paper presents the modular chromatic number of , and we obtain a new relation, .

Keywords: Modular kColoring, Modular Chromatic Number, Vertex Color Sum, Corona Product, Generalized Jahangir Graph

References

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Copyright

© 2023 Sumathi & Tamilselvi. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)