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On Vertex-Edge and Independent Vertex-Edge Domination

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Combinatorial Optimization and Applications (COCOA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11949))

Abstract

Given a graph \(G = (V,E)\), a vertex \(u \in V\) ve-dominates all edges incident to any vertex of \(N_G[u]\). A set \(S \subseteq V\) is a ve-dominating set if for all edges \(e\in E\), there exists a vertex \(u \in S\) such that u ve-dominates e. Lewis [Ph.D. thesis, 2007] proposed a linear time algorithm for ve-domination problem for trees. In this paper, first we have constructed an example where the proposed algorithm fails. Then we have proposed a linear time algorithm for ve-domination problem in block graphs, which is a superclass of trees. We have also proved that finding minimum ve-dominating set is NP-complete for undirected path graphs. Finally, we have characterized the trees with equal ve-domination and independent ve-domination number.

K. Ranjan—This work was done when the second author was persuing his M.Tech. at IIT Patna.

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Author information

Authors and Affiliations

  1. Department of Mathematics, IIT Patna, Bihta, India

    Subhabrata Paul

  2. Department of Computer Science and Engineering, IIT Madras, Chennai, India

    Keshav Ranjan

Authors
  1. Subhabrata Paul
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  2. Keshav Ranjan
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Correspondence to Subhabrata Paul .

Editor information

Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Yingshu Li

  2. Florida Atlantic University, Boca Raton, FL, USA

    Mihaela Cardei

  3. Kennesaw State University, Marietta, GA, USA

    Yan Huang

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Paul, S., Ranjan, K. (2019). On Vertex-Edge and Independent Vertex-Edge Domination. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_35

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  • DOI: https://doi.org/10.1007/978-3-030-36412-0_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36411-3

  • Online ISBN: 978-3-030-36412-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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