Domination Parameters of a Graph and its Complement

Domination Parameters of a Graph and its Complement

A dominating set in a graph is a set of vertices such that every vertex in ( ) \ is adjacent to at least one vertex in , and the domination number of is the minimum cardinality of a dominating set of . Placing constraints on a dominating set yields different domination parameters, including total, c...

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Bibliographic Details
Published in:Discussiones Mathematicae. Graph Theory Vol. 38; no. 1; pp. 203 - 215
Main Authors: Desormeaux, Wyatt J., Haynes, Teresa W., Henning, Michael A.
Format: Journal Article
Language:English
Published: De Gruyter Open 01-01-2018
University of Zielona Góra
Subjects:
05C69
clique domination
complement
connected domination
domination
restrained domination
total domination
Online Access:Get full text
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Summary:A dominating set in a graph is a set of vertices such that every vertex in ( ) \ is adjacent to at least one vertex in , and the domination number of is the minimum cardinality of a dominating set of . Placing constraints on a dominating set yields different domination parameters, including total, connected, restrained, and clique domination numbers. In this paper, we study relationships among domination parameters of a graph and its complement.
ISSN:1234-3099
2083-5892
DOI:10.7151/dmgt.2002