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Vertex-Edge Domination in Unit Disk 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

Let \(G=(V,E)\) be a simple graph. A set \(D \in V\) is called a vertex-edge dominating set of G if for each edge \(e=(u,v)\in E\), either u or v is in D or one vertex from their neighbor is in D. Simply, a vertex \(v\in V\), vertex-edge dominates every edge (u, v), as well as every edge adjacent to these edges. The vertex-edge dominating problem is to find a minimum vertex-edge dominating set of G. Herein, we study the vertex-edge dominating set problem in unit disk graphs and prove that this problem is NP-hard in that class of graphs. We also show that the problem admits a polynomial time approximation scheme (PTAS) in unit disk graphs.

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Authors and Affiliations

  1. Indian Institute of Technology, Guwahati, Guwahati, India

    Sangram K. Jena & Gautam K. Das

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  1. Sangram K. Jena
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  2. Gautam K. Das
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Correspondence to Gautam K. Das .

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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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Jena, S.K., Das, G.K. (2020). Vertex-Edge Domination in Unit Disk 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_6

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  • DOI: https://doi.org/10.1007/978-3-030-39219-2_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-39218-5

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