ISSN : 2663-2187

The Total Certified Domination Number for Indu-Bala Product of Some Graphs

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A.Janani, J. Befija Minnie, A. Jancy Vini
» doi: 10.48047/AFJBS.6.12.2024.4316-4322

Abstract

The Total Certified Domination Number aims for a balance between the concepts Certified domination and Total Domination providing better coverage with fewer dominating vertices. A total dominating et ???? is said to be total certified dominating set if every vertex in D has zero or at least two neighbours in ???? (????) − ????.The minimumcardinality of a total certified dominating set is called the Total Certified Number and is denoted by???????????????????? (????). This total certified domination concept provides a different approach to calculate the number of vertices required to dominate the paths and cycles based on the residue of ????1 modulo 4.For the two graphs????1 and????2,the Indu-Bala product????1 ▼ ????2 be given from two disjoint copies of the join????1⋁????2where the corresponding vertices of two copies of????2are connected by an edge.In this article, the total certified domination concept is applied in Indu-Bala Product for some standard graphs and some important results and theorems are derived based on the findings.

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