k-Adjacency Domination in Graphs

Document Type : Original Article

Author

Assistant Professor, Department of Computer Science, Bojnourd University, Bojnourd, Iran

Abstract

Let be a simple and undirected graph with vertex set . A set is called a dominating set of if every vertex
outside is adjacent to at least one vertex of . For any integer , a dominating set is called a -adjacency
dominating set of if the induced subgraph contains at least one vertex of degree at most . The minimum
cardinality of a - adjacency dominating set of is called the - adjacency domination number of that is
denoted by . In this paper, the study of - adjacency domination in graphs is initiated, and exact values and
some bounds on the - adjacency domination number of a given graph are presented. Furthermore, it is
shown that there is a polynomial-time algorithm that computes the -adjacency domination number of a
given tree. Moreover, it is proven that the decision problem associated to the -adjacency domination is
NP-complete for bipartite graphs.

Keywords

References

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Electronic and Cyber Defense
Volume 9, Issue 3 - Serial Number 35
Serial No. 35, Autumn Quarterly
December 2021
Pages 125-131

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History

  • Receive Date: 16 December 2020
  • Revise Date: 01 February 2021
  • Accept Date: 25 February 2021
  • Publish Date: 22 November 2021

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