Domination Defect in Graphs: Guarding With Fewer Guards

Angsuman Das () and Wyatt J. Desormeaux ()
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Angsuman Das: St. Xavier’s College
Wyatt J. Desormeaux: University of Johannesburg

Indian Journal of Pure and Applied Mathematics, 2018, vol. 49, issue 2, 349-364

Abstract: 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.

Keywords: Minimum dominating set; efficient dominating set; vertex removal; changing domination; domination defect (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s13226-018-0273-8

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