Topological structures induced by chromatic partitioning of vertex set of graphs

K. Lalithambigai and P. Gnanachandra
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 3, Pages 620–634
DOI: 10.7546/nntdm.2023.29.3.620-634
Full paper (PDF, 207 Kb)

Details

Authors and affiliations

K. Lalithambigai
Department of Mathematics, Sri Kaliswari College
(Autonomous, affiliated to Madurai Kamaraj University)
Sivakasi – 626130, Tamilnadu, India

P. Gnanachandra
Centre for Research and Post Graduate Studies in Mathematics, Ayya Nadar Janaki Ammal College
(Autonomous, affiliated to Madurai Kamaraj University)
Sivakasi – 626124, Tamilnadu, India

Abstract

This paper presents a method of constructing topologies on vertex set of a graph induced by chromatic partition of vertex set of the graph. It introduces colour lower approximation and colour upper approximation of vertex induced subgraphs and acquaints the open and closed sets of the topology generated by chromatic partition on the vertex set of graphs. It explores some of the properties of colour lower approximation and colour upper approximation of vertex induced subgraphs. It also establishes some new subgraphs based on the colour lower approximation and colour upper approximation and some of their properties have been studied.

Keywords

• Vertex colouring
• Chromatic partition
• Colour lower approximation
• Colour upper approximation
• Graph chromatic topological space

2020 Mathematics Subject Classification

• 57M15
• 54A05
• 54A10
• 54H99
• 05C15

References

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Manuscript history

• Received: 20 November 2022
• Revised: 16 May 2023
• Accepted: 14 August 2023
• Online First: 8 September 2023

Copyright information

Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).