Complexity and approximation ratio of semitotal domination in graphs

Document Type : Original paper

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Guangzhou University

Abstract

A set S⊆V(G) is a semitotal dominating set of a graph G if it is a dominating set of G and every vertex in S is within distance 2 of another vertex of S. The semitotal domination number γt2(G) is the minimum cardinality of a semitotal dominating set of G. We show that the semitotal domination problem is APX-complete for bounded-degree graphs, and the semitotal domination problem in any graph of maximum degree Δ can be approximated with an approximation ratio of 2+ln⁡(Δ−1).

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References

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Communications in Combinatorics and Optimization
Volume 3, Issue 2
December 2018
Pages 143-150

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