Equitable Color Class Domination Number of Honeycomb Networks Graph and Inverse Equitable Color Class Domination Number of a Graph

• Published in: Indian journal of science and technology Vol. 17; no. 36; pp. 3800 - 3810
• Main Authors: Esakkimuthu, A, Selvam, S Mari
• Format: Journal Article
• Language: English
• Published: 25.09.2024
• ISSN: 0974-6846
• DOI: 10.17485/IJST/v17i36.2458

Objectives: In this study, we find a new graph domination parameter named “Inverse Equitable Color Class Domination” and discuss the equitable color class domination number of honeycomb networks graph. Methods: Let be a connected graph. Assume a group containing colors. Let be an equitably colorable function. A dominating subset of is called an equitable color class dominating set if the number of dominating nodes in each color class is equal. The least possible cardinality of an equitable color class dominating set of is the equitable color class domination number itself. It is indicated by . If there exists another equitable color class dominating set in is called an inverse equitable color class dominating set of corresponding to . It is indicated by . Findings: In this paper we conclude the equitable color class domination number of honeycomb networks, honeycomb cup networks graphs and the inverse equitable color class domination number of some graphs. Novelty: This study introduces the concept of “Inverse Equitable Color Class Domination in Graphs”. It obtains many bounds in terms of nodes, links, and other different parameters. 2020 Mathematics Subject Classification: 05C15, 05C69 Keywords: Dominating Set, Equitable Coloring, Color Class (CC), Equitable Color Class (ECC), Equitable Color Class Dominating Set, Inverse Equitable Color Class Domination Number