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The Connected Domination Number of Grids

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Book cover Algorithms and Discrete Applied Mathematics (CALDAM 2021)

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Abstract

Closed form expressions for the domination number of an \(n \times m\) grid have attracted significant attention, and an exact expression has been obtained in 2011 [7]. In this paper, we present our results on obtaining new lower bounds on the connected domination number of an \(n \times m\) grid. The problem has been solved for grids with up to 4 rows and with 6 rows and the best currently known lower bound for arbitrary m, n is  [11]. Fujie [4] came up with a general construction for a connected dominating set of an \(n \times m\) grid. In this paper, we investigate whether this construction is indeed optimum. We prove a new lower bound of for arbitrary \(m,n \ge 4\).

This research was supported by the first author’s INSPIRE fellowship from Department of Science and Technology (DST), Govt. of India.

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Authors and Affiliations

  1. Indian Institute of Science Education and Research (IISER) Pune, Pune, India

    Adarsh Srinivasan

  2. Indian Institute of Technology (IIT) Madras, Chennai, India

    N. S. Narayanaswamy

Authors
  1. Adarsh Srinivasan
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  2. N. S. Narayanaswamy
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Correspondence to Adarsh Srinivasan .

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Editors and Affiliations

  1. Indian Institute of Technology Ropar, Rupnagar, India

    Apurva Mudgal

  2. Institute of Mathematical Sciences, Chennai, India

    C. R. Subramanian

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Srinivasan, A., Narayanaswamy, N.S. (2021). The Connected Domination Number of Grids. In: Mudgal, A., Subramanian, C.R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2021. Lecture Notes in Computer Science(), vol 12601. Springer, Cham. https://doi.org/10.1007/978-3-030-67899-9_19

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  • DOI: https://doi.org/10.1007/978-3-030-67899-9_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-67898-2

  • Online ISBN: 978-3-030-67899-9

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