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Pitchfork Domination in Graphs by Al-Harere, Manal N.; Abdlhusein, Mohammed A. is a Computer Science article available to read on EtoBox.

What is Pitchfork Domination in Graphs about?

In this paper, a new model of domination in graphs called the pitchfork domination is introduced. Let [Formula: see text] be a finite, simple and undirected graph without isolated vertices, a subset [Formula: see text] of [Formula: see text] is a pitchfork dominating set if every vertex [Formula: see text] dominates at least [Formula: see text] and at most [Formula: see text] vertices of [Formula: see text], where [Formula: see text] and [Formula: see text] are non-negative integers. The domination number of [Formula: see text], denotes [Formula: see text] is a minimum cardinality over all pitchfork dominating sets in [Formula: see text]. In this work, pitchfork domination when [Formula: see text] and [Formula: see text] is studied. Some bounds on [Formula: see text] related to the order, size, minimum degree, maximum degree of a graph and some properties are given. Pitchfork domination is determined for some known and new modified graphs. Finally, a question has been answered and discussed that; does every finite, simple and undirected graph [Formula: see text] without isolated vertices have a pitchfork domination or not?

Who reads Pitchfork Domination in Graphs?

Author

Al-Harere, Manal N.; Abdlhusein, Mohammed A.

Publisher

World Scientific ; World Scientific Publishing Co. Pte Ltd; World Scientific Pub Co Pte Lt (ISSN 1793-8309)

Published

2020

Language

EN

Field

Computer Science (Physical Sciences)