International Journal of Nonlinear Analysis and Applications

The arrow domination in graphs

Document Type : Research Paper

Authors

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

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

Abstract

‎The arrow domination is introduced in this paper with its inverse as a new type of domination‎. Let G be a finite graph‎, ‎undirected‎, ‎simple and has no isolated vertex‎, ‎a set D of V(G) is said an arrow dominating set if |N(w)∩(V−D)|=i and |N(w)∩D|≥j for every w∈D such that i and j are two non-equal positive integers‎. ‎The arrow domination number γar(G) is the minimum cardinality over all arrow dominating sets in G‎. ‎Essential properties and bounds of arrow domination and its inverse when i=1 and j=2 are proved‎. ‎Then‎, ‎arrow domination number is discussed for several standard graphs and other graphs that formed by join and corona operations‎.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 473-480
  • Receive Date: 10 December 2020
  • Revise Date: 13 January 2021
  • Accept Date: 04 February 2021