Generalizing TCCD-Number For Power Graph Of Some Graphs

S Kaviya; G Mahadevan; C Sivagnanam

doi:10.17485/IJST/v17sp1.243

Article

Generalizing TCCD-Number For Power Graph Of Some Graphs

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17sp1.243

Year: 2024, Volume: 17, Issue: Special Issue 1, Pages: 115-123

Original Article

Generalizing TCCD-Number For Power Graph Of Some Graphs

S Kaviya^1*, G Mahadevan¹, C Sivagnanam²

¹Department of Mathematics, Gandhigram Rural Institute - Deemed to be University, Gandhigram, Tamil Nadu
²Mathematics and Computing Skills Unit, University of Technology and Applied Sciences-Sur, Sultanate of Oman

*Corresponding Author
Email: [email protected]

Received Date:29 August 2023, Accepted Date:05 March 2024, Published Date:31 May 2024

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

Abstract

Objective: Finding the triple connected certified domination number for the power graph of some peculiar graphs. Methods: A dominating set with the condition that every vertex in has either zero or at least two neighbors in and is triple connected is a called triple connected certified domination number of a graph. The minimum cardinality among all the triple connected certified dominating sets is called the triple connected certified domination number and is denoted by . The upper bound and lower bound of for the given graphs is found and then proved the upper bound and lower bound of were equal. Findings: We found the (TCCD)-number for the power graph of some peculiar graphs. Also, we have generalized the result for path, cycle, ladder graph, comb graph, coconut tree graph, triangular snake, alternate triangular snake, quadrilateral snake and tadpole graph. Novelty: The triple connected certified domination is a new parameter in which the certified domination holds the triple connected in induced .

Keywords: Domination Number, Power Graphs, Triple Connected, Certified Domination, Triple Connected Certified Domination

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Copyright

© 2024 Kaviya et al. 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)