A STUDY ON PERFECT ITALIAN DOMINATION OF GRAPHS AND THEIR COMPLEMENTS

Title

A STUDY ON PERFECT ITALIAN DOMINATION OF GRAPHS AND THEIR COMPLEMENTS

Creator

Poovathingal, Agnes; Kureethara, Joseph Varghese

Description

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 0s. 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 NordhausGaddum type inequalities in the Perfect Italian Domination number are also discussed. 2025, Krasovskii Institute of Mathematics and Mechanics. All rights reserved.

Source

Ural Mathematical Journal;Volume;11;Issue;1;pp.104-113

Date

01-01-2025

Publisher

Krasovskii Institute of Mathematics and Mechanics

Subject

Graph complement; NordhausGaddum type inequalities; Perfect Italian domination

Coverage

Poovathingal A., Christ University, Karnataka, Bangalore, 560029, India, Christ College (Autonomous), Christ Nagar, Kerala, Irinjalakuda, 680125, India; Kureethara J.V., Christ University, Karnataka, Bangalore, 560029, India, Kuriakose Elias College, Kottayam, Kerala, Mannanam, 686561, India

Rights

All Open Access; Gold Open Access; Green Open Access

Relation

ISSN: 24143952;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.15826/umj.2025.1.007

https://www.scopus.com/pages/publications/105012559878?origin=resultslist