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Algorithmic aspects of k-tuple total domination in graphs

Pradhan, D (2012) Algorithmic aspects of k-tuple total domination in graphs. In: INFORMATION PROCESSING LETTERS, 112 (21). pp. 816-822.

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Official URL: http://dx.doi.org/10.1016/j.ipl.2012.07.010

Abstract

For a fixed positive integer k, a k-tuple total dominating set of a graph G = (V. E) is a subset T D-k of V such that every vertex in V is adjacent to at least k vertices of T Dk. In minimum k-tuple total dominating set problem (MIN k-TUPLE TOTAL DOM SET), it is required to find a k-tuple total dominating set of minimum cardinality and DECIDE MIN k-TUPLE TOTAL DOM SET is the decision version of MIN k-TUPLE TOTAL DOM SET problem. In this paper, we show that DECIDE MIN k-TUPLE TOTAL DOM SET is NP-complete for split graphs, doubly chordal graphs and bipartite graphs. For chordal bipartite graphs, we show that MIN k-TUPLE TOTAL DOM SET can be solved in polynomial time. We also propose some hardness results and approximation algorithms for MIN k-TUPLE TOTAL DOM SET problem. (c) 2012 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to Elsevier
Keywords: Graph algorithms; Domination; Total domination; k-Tuple total domination; NP-complete; APX-complete
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 31 Jan 2013 12:44
Last Modified: 31 Jan 2013 12:44
URI: http://eprints.iisc.ac.in/id/eprint/45336

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