ISSN : 2663-2187

Domination in Edge Product Cluster Hypergraphs

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Mary Christal Flower. C , Befija Minnie. J , Jancy Vini. J
» doi: 10.48047/AFJBS.6.15.2024.102-111

Abstract

The study on Domination in Edge Product Cluster Hypergraph aims for a balance between the concepts of Domination and Edge Product in Cluster Hypergraphs. The cluster hypergraph ???? = (????????,????) is said to be an Edge Product Cluster Hypergraph if there exists an edge function ????:???? → ???? such that the edge function ???? and the corresponding edge product function ???? of ???? on ???????? have the following conditions are ????(????) ∈ ???? for every ???? ∈ ???????? and if ????(????1 ) × ????(????2 ) × . . .× ????(???????? ) ∈ ???? for some edges ????1 , ????2 , . . . ???????? ∈ ????(????) then the edges ????1 , ????2 , . . . ???????? are all adjacent to some vertex ???????? . This article explores the concept of Domination in Edge Product Cluster Hypergraphs. It is demonstrated that every dominating set in ???? contains atleast two vertices. Also, some theorems related to the concept of Domination in Edge product Cluster Hypergraphs have been discussed and demonstrated here.

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