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Laplacian Controllability for Graphs Obtained by Some Standard Products

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Abstract

Let \(L_G\) be the Laplacian matrix of a graph G with n vertices, and let \({\mathbf {b}}\) be a binary vector of length n. The pair \((L_G, {\mathbf {b}})\) is said to be controllable (and we also say that G is Laplacian controllable for \({\mathbf {b}}\)) if \(L_G\) has no eigenvector orthogonal to \({\mathbf {b}}\). In this paper we study the Laplacian controllability of joins, Cartesian products, tensor products and strong products of two graphs. Besides some theoretical results, we give an iterative construction of infinite families of controllable pairs \((L_G, {\mathbf {b}})\).

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Acknowledgements

Research is partially supported by Serbian Ministry of Education, Science and Technological Development, via Faculty of Mathematics, University of Belgrade, and by INDAM-GNSAGA (Italy).

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Authors and Affiliations

  1. Department of Mathematics, Kuwait University, 13060, Safat, Kuwait

    Milica Anđelić

  2. Department of Mathematics, University of Naples ‘Federico II’, P. le Tecchio 80, 80125, Naples, Italy

    Maurizio Brunetti

  3. Faculty of Mathematics, University of Belgrade, Studentski trg 16, Belgrade, 11 000, Serbia

    Zoran Stanić

Authors
  1. Milica Anđelić
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  2. Maurizio Brunetti
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  3. Zoran Stanić
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Correspondence to Zoran Stanić.

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Anđelić, M., Brunetti, M. & Stanić, Z. Laplacian Controllability for Graphs Obtained by Some Standard Products. Graphs and Combinatorics 36, 1593–1602 (2020). https://doi.org/10.1007/s00373-020-02212-6

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  • DOI: https://doi.org/10.1007/s00373-020-02212-6

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