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Domination Defect in Graphs: Guarding With Fewer Guards

Author

Listed:
  • Angsuman Das

    (St. Xavier’s College)

  • Wyatt J. Desormeaux

    (University of Johannesburg)

Abstract

In this paper, we introduce a new graph parameter called the domination defect of a graph. The domination number γ of a graph G is the minimum number of vertices required to dominate the vertices of G. Due to the minimality of γ, if a set of vertices of G has cardinality less than γ then there are vertices of G that are not dominated by that set. The k-domination defect of G is the minimum number of vertices which are left un-dominated by a subset of γ - k vertices of G. We study different bounds on the k-domination defect of a graph G with respect to the domination number, order, degree sequence, graph homomorphisms and the existence of efficient dominating sets. We also characterize the graphs whose domination defect is 1 and find exact values of the domination defect for some particular classes of graphs.

Suggested Citation

  • Angsuman Das & Wyatt J. Desormeaux, 2018. "Domination Defect in Graphs: Guarding With Fewer Guards," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(2), pages 349-364, June.
    • Handle: RePEc:spr:indpam:v:49:y:2018:i:2:d:10.1007_s13226-018-0273-8
    DOI: 10.1007/s13226-018-0273-8
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