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The general position number of integer lattices

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  • Klavžar, Sandi
  • Rus, Gregor

Abstract

The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic. The n-dimensional grid graph P∞n is the Cartesian product of n copies of the two-way infinite path P∞. It is proved that if n∈N, then gp(P∞n)=22n−1. The result was earlier known only for n ∈ {1, 2} and partially for n=3.

Suggested Citation

  • Klavžar, Sandi & Rus, Gregor, 2021. "The general position number of integer lattices," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320306172
    DOI: 10.1016/j.amc.2020.125664
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    References listed on IDEAS

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    1. Anand, Bijo S. & Chandran S. V., Ullas & Changat, Manoj & Klavžar, Sandi & Thomas, Elias John, 2019. "Characterization of general position sets and its applications to cographs and bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 84-89.
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    Cited by:

    1. Cicerone, Serafino & Di Stefano, Gabriele & Klavžar, Sandi, 2023. "On the mutual visibility in Cartesian products and triangle-free graphs," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    2. Tian, Jing & Xu, Kexiang, 2021. "The general position number of Cartesian products involving a factor with small diameter," Applied Mathematics and Computation, Elsevier, vol. 403(C).

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    1. Cicerone, Serafino & Di Stefano, Gabriele & Klavžar, Sandi, 2023. "On the mutual visibility in Cartesian products and triangle-free graphs," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    2. Tian, Jing & Xu, Kexiang, 2021. "The general position number of Cartesian products involving a factor with small diameter," Applied Mathematics and Computation, Elsevier, vol. 403(C).
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