Algorithmic aspects of disjunctive domination in graphs [article]

B.S. Panda, Arti Pandey, S. Paul
2015 arXiv   pre-print
For a graph G=(V,E), a set D⊆ V is called a disjunctive dominating set of G if for every vertex v∈ V∖ D, v is either adjacent to a vertex of D or has at least two vertices in D at distance 2 from it. The cardinality of a minimum disjunctive dominating set of G is called the disjunctive domination number of graph G, and is denoted by γ_2^d(G). The Minimum Disjunctive Domination Problem (MDDP) is to find a disjunctive dominating set of cardinality γ_2^d(G). Given a positive integer k and a graph
more » ... , the Disjunctive Domination Decision Problem (DDDP) is to decide whether G has a disjunctive dominating set of cardinality at most k. In this article, we first propose a linear time algorithm for MDDP in proper interval graphs. Next we tighten the NP-completeness of DDDP by showing that it remains NP-complete even in chordal graphs. We also propose a ((Δ^2+Δ+2)+1)-approximation algorithm for MDDP in general graphs and prove that MDDP can not be approximated within (1-ϵ) (|V|) for any ϵ>0 unless NP ⊆ DTIME(|V|^O( |V|)). Finally, we show that MDDP is APX-complete for bipartite graphs with maximum degree 3.
arXiv:1502.07718v2 fatcat:iixjzu637vcd5ldwx7dzmxc5hu