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Strong Geodetic Number of Complete Bipartite Graphs, Crown Graphs and Hypercubes

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Abstract

The strong geodetic number, \(\text {sg}(G),\) of a graph G is the smallest number of vertices such that by fixing a suitable geodesic between each pair of selected vertices, all vertices of the graph are covered. In this paper, the formula for \(\text {sg}(K_{n,m})\) is given, as well as a formula for the crown graphs \(S_n^0\). Bounds on the strong geodetic number of the hypercube \(Q_n\) are also discussed.

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Acknowledgements

The authors would like to thank Sandi Klavžar and Matjaž Konvalinka for a number of fruitful conversations, and also anonymous referees for many helpful comments.

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Authors and Affiliations

  1. Université Lyon 1, LIRIS UMR CNRS 5205, Univ Lyon, 69621, Lyon, France

    Valentin Gledel

  2. Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia

    Vesna Iršič

  3. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Vesna Iršič

Authors
  1. Valentin Gledel
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  2. Vesna Iršič
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Correspondence to Vesna Iršič.

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Communicated by Sanming Zhou.

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Gledel, V., Iršič, V. Strong Geodetic Number of Complete Bipartite Graphs, Crown Graphs and Hypercubes. Bull. Malays. Math. Sci. Soc. 43, 2757–2767 (2020). https://doi.org/10.1007/s40840-019-00833-6

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  • DOI: https://doi.org/10.1007/s40840-019-00833-6

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