Captive domination in graphs-Reference-Cited by-同舟云学术

Captive domination in graphs

Published:2020-07-17 Issue:06 Volume:12 Page:2050076
ISSN:1793-8309
Container-title:Discrete Mathematics, Algorithms and Applications
language:en
Short-container-title:Discrete Math. Algorithm. Appl.

Author:

Al-Harere Manal N.¹^ORCID,Omran Ahmed A.²,Breesam Athraa T.¹

Affiliation:

1. Department of Applied Sciences, University of Technology, Baghdad, Iraq

2. Department of Mathematics, College of Education for Pure Science, University of Babylon, Babylon, Iraq

Abstract

In this paper, a new definition of graph domination called “Captive Domination” is introduced. The proper subset of the vertices of a graph [Formula: see text] is a captive dominating set if it is a total dominating set and each vertex in this set dominates at least one vertex which doesn’t belong to the dominating set. The inverse captive domination is also introduced. The lower and upper bounds for the number of edges of the graph are presented by using the captive domination number. Moreover, the lower and upper bounds for the captive domination number are found by using the number of vertices. The condition when the total domination and captive domination number are equal to two is discussed and obtained results. The captive domination in complement graphs is discussed. Finally, the captive dominating set of paths and cycles are determined.

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793830920500767

Reference19 articles.

1. Pitchfork domination in graphs

2. Further results on bi-domination in graphs

3. Tadpole Domination in Graphs

4. Total domination in graphs

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