An inverse triple effect domination in graphs

Document Type : Research Paper

Authors

Department of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, Iraq

Abstract

In this paper, an inverse triple effect domination is introduced for any finite graph G=(V,E) simple and undirected without isolated vertices. A subset D1 of VD is an inverse triple effect dominating set if every vD1 dominates exactly three vertices of VD1. The inverse triple effect domination number γte1(G) is the minimum cardinality over all inverse triple effect dominating sets in G. Some results and properties on γte1(G) are given and proved. Under any conditions the graph satisfies γte(G)+γte1(G)=n is studied. Lower and upper bounds for the size of a graph that has γte1(G) are putted in two cases when D1=VD and when D1VD. Which properties of a vertex to be belongs to D1 or out of it are discussed. Then, γte1(G) is evaluated and proved for several graphs.

Keywords

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Volume 12, Issue 2
November 2021
Pages 913-919
  • Receive Date: 06 February 2021
  • Revise Date: 26 March 2021
  • Accept Date: 03 April 2021