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Get Free AccessPerfect 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.
Agnes Poovathingal, Joseph Varghese Kureethara (2025). A STUDY ON PERFECT ITALIAN DOMINATION OF GRAPHS AND THEIR COMPLEMENTS. , 11(1), DOI: https://doi.org/10.15826/umj.2025.1.007.
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Type
Article
Year
2025
Authors
2
Datasets
0
Total Files
0
Language
en
DOI
https://doi.org/10.15826/umj.2025.1.007
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