EXTRACTING TRIPLE CONNECTED CERTIFIED DOMINATION NUMBER FOR THE STRONG PRODUCT OF PATHS AND CYCLES

EXTRACTING TRIPLE CONNECTED CERTIFIED DOMINATION NUMBER FOR THE STRONG PRODUCT OF PATHS AND CYCLES

G. Mahadevan, S. Kaviya, C. Sivagnanam

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Abstract

A dominating set S of a graph G is said to be a triple connected certified dominating set (TCCD - set) if for every vertex v ∈ S, | N(v) ∩ (V −S) | ̸= 1 and ⟨S⟩ is triple connected. The minimum cardinality of a TCCD - set is called the triple connected certified domination number (TCCD - number) and is denoted by γTCC(G). The novelty of triple connected certified domination number is which the certified domination holds the triple connected in induced S. The upper bound and loweer bound of γTCC for the given graphs is found and then proved that the upper bound and lower bound of γTCC were equal. This article investigates the TCCD number for the strong product of paths and cycles.

Keywords

Domination number, certified domination, triple connected, triple connected certified domination, product graphs, cycle.