Please use this identifier to cite or link to this item: http://dspace.iitrpr.ac.in:8080/xmlui/handle/123456789/3296
Title: Semipaired domination in some subclasses of chordal graphs
Authors: Henning, M. A.
Pandey, A.
Tripathi, V.
Keywords: Domination
Semipaired domination
Block graphs
NP-completeness
Graph algorithms
Issue Date: 6-Dec-2021
Abstract: A dominating set D of a graph G without isolated vertices is called semipaired dominating set if D can be partitioned into 2-element subsets such that the vertices in each set are at distance at most 2. The semipaired domination number, denoted by γpr2(G) is the minimum cardinality of a semipaired dominating set of G. Given a graph G with no isolated vertices, the MINIMUM SEMIPAIRED DOMINATION problem is to find a semipaired dominating set of G of cardinality γpr2(G). The decision version of the MINIMUM SEMIPAIRED DOMINATION problem is already known to be NP-complete for chordal graphs, an important graph class. In this paper, we show that the decision version of the MINIMUM SEMIPAIRED DOMINATION problem remains NP-complete for split graphs, a subclass of chordal graphs. On the positive side, we propose a linear-time algorithm to compute a minimum cardinality semipaired dominating set of block graphs. In addition, we prove that the MINIMUM SEMIPAIRED DOMINATION problem is APX-complete for graphs with maximum degree 3
URI: http://localhost:8080/xmlui/handle/123456789/3296
Appears in Collections:Year-2021

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