A STUDY ON PERFECT ITALIAN DOMINATION OF GRAPHS AND THEIR COMPLEMENTS

Agnes Poovathingal     (Christ University, Bangalore-560029, Karnataka; Christ College (Autonomous), Christ Nagar, Irinjalakuda, Kerala 680125, India)
Joseph Varghese Kureethara     (Christ University, Bangalore-560029, Karnataka; Kuriakose Elias College, Kottayam, Mannanam, Kerala 686561, India)

Abstract


Perfect Italian Domination is a type of vertex domination  which can also be viewed as a graph labelling problem. The vertices of a graph \(G\) are labelled by 0, 1 or 2 in such a way that a vertex labelled 0 should have a neighbourhood with exactly two vertices in it labelled 1 each or with exactly one vertex labelled 2. The remaining vertices in the neighbourhood of the vertex labelled 0 should be all 0's. The minimum sum of all labels of the graph G  satisfying these conditions is called its Perfect Italian domination number. We study the behaviour of graph complements and how the Perfect Italian Domination number varies between a graph and its complement. The Nordhaus–Gaddum type inequalities in the Perfect Italian Domination number are also discussed.

Keywords


Perfect Italian domination, Graph complement, Nordhaus–Gaddum type inequalities

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References


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DOI: http://dx.doi.org/10.15826/umj.2025.1.007

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