Journal of Applied Mathematics and Computing

, Volume 43, Issue 1, pp 133–150

Minimum 2-tuple dominating set of permutation graphs

  • Sambhu Charan Barman
  • Sukumar Mondal
  • Madhumangal Pal
Original Research

DOI: 10.1007/s12190-013-0656-2

Cite this article as:
Barman, S.C., Mondal, S. & Pal, M. J. Appl. Math. Comput. (2013) 43: 133. doi:10.1007/s12190-013-0656-2

Abstract

For a fixed positive integer k, a k-tuple dominating set of a graph G=(V,E) is a subset DV such that every vertex in V is dominated by at least k vertex in D. The k-tuple domination number γ×k(G) is the minimum size of a k-tuple dominating set of G. The special case when k=1 is the usual domination. The case when k=2 was called double domination or 2-tuple domination. A 2-tuple dominating set D2 is said to be minimal if there does not exist any D′⊂D2 such that D′ is a 2-tuple dominating set of G. A 2-tuple dominating set D2, denoted by γ×2(G), is said to be minimum, if it is minimal as well as it gives 2-tuple domination number. In this paper, we present an efficient algorithm to find a minimum 2-tuple dominating set on permutation graphs with n vertices which runs in O(n2) time.

Keywords

Design of algorithmsAnalysis of algorithmsDominationk-Tuple domination2-Tuple dominationPermutation graphs

Mathematics Subject Classification

05C78

Copyright information

© Korean Society for Computational and Applied Mathematics 2013

Authors and Affiliations

  • Sambhu Charan Barman
    • 1
  • Sukumar Mondal
    • 2
  • Madhumangal Pal
    • 1
  1. 1.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia
  2. 2.Department of MathematicsRaja N.L. Khan Women’s CollegeMidnaporeIndia