Exploration of CCD-Number for Some Specific Graphs

G Mahadevan; K Priya; C Sivagnanam

doi:10.17485/IJST/v17sp1.274

Article

Exploration of CCD-Number for Some Specific Graphs

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17sp1.274

Year: 2024, Volume: 17, Issue: Special Issue 1, Pages: 144-148

Original Article

Exploration of CCD-Number for Some Specific Graphs

G Mahadevan^1*, K Priya¹, C Sivagnanam²

¹Department of Mathematics, The Gandhigram Rural Institute - Deemed to be University, Gandhigram, Tamil Nadu, India
²Mathematics and Computing Skills Unit, 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

Objectives: A dominating set S of a graph G is said to be a complementary corona dominating set (CCD-set) if every vertex in is either a pendent vertex or a support vertex. The smallest cardinality of a CCD-set is called the CCD-number and is denoted by . In this article, we explore the CCD-number for some specific graphs. Methods: We are finding the upper bound of and the lower bound of . We prove that both the upper and lower bound are equal for the given graphs. Findings: In this article, we obtained the CCD-number for some specific graphs. Novelty: Complementary corona dominating set is a vertex set such that the induced subgraph of the complementary set is isomorphic to corona virus.

Keywords: Dominating Set, Corona Dominating Set, Support And Pendent Vertex, Butterfly Graph, Dumbbell Graph, Coconut Tree Graph, Peacock Head Graph, Sunlet Graph, Spider Graph, Firecracker Graph, Uniform g-ply graph

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Copyright

© 2024 Mahadevan 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)