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Hardness Results of Global Total k-Domination Problem in Graphs

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Algorithms and Discrete Applied Mathematics (CALDAM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12016))

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Abstract

A set \( D \subseteq V_{G} \) of a graph \( G = (V_{G},E_{G}) \) is called a global total k-dominating set of G if D is a total k-dominating set of both G and \( \overline{G} \), the complement of G. The Minimum Global Total k-Domination problem is to find a global total k-dominating set of minimum cardinality of the input graph G and Decide Global Total k-Domination problem is the decision version of Minimum Global Total k-Domination problem. The Decide Global Total k -Domination problem is known to be NP-complete for general graphs. In this paper, we study the complexity of the Minimum Global Total k-Domination problem. We show the Decide Global Total k-Domination problem remains NP-complete for bipartite graphs and chordal graphs. Next, we show that the Minimum Global Total k-Domination problem admits a constant approximation algorithm for bounded degree graphs. Finally, we show that the Minimum Global Total k-Domination problem is APX-complete for bounded degree graphs.

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Authors and Affiliations

  1. Computer Science and Application Group, Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016, India

    B. S. Panda & Pooja Goyal

Authors
  1. B. S. Panda
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  2. Pooja Goyal
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Correspondence to B. S. Panda .

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Editors and Affiliations

  1. University of Kerala, Thiruvananthapuram, India

    Manoj Changat

  2. Indian Statistical Institute, Kolkata, India

    Sandip Das

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Panda, B.S., Goyal, P. (2020). Hardness Results of Global Total k-Domination Problem in Graphs. In: Changat, M., Das, S. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2020. Lecture Notes in Computer Science(), vol 12016. Springer, Cham. https://doi.org/10.1007/978-3-030-39219-2_8

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  • DOI: https://doi.org/10.1007/978-3-030-39219-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-39218-5

  • Online ISBN: 978-3-030-39219-2

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