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Mutual-visibility and general position in double graphs and in Mycielskians

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  • Roy, Dhanya
  • Klavžar, Sandi
  • Lakshmanan S, Aparna

Abstract

The general position problem in graphs is to find the largest possible set of vertices with the property that no three of them lie on a common shortest path. The mutual-visibility problem in graphs is to find the maximum number of vertices that can be selected such that every pair of vertices in the collection has a shortest path between them with no vertex from the collection as an internal vertex. Here, the general position problem and the mutual-visibility problem are investigated in double graphs and in Mycielskian graphs. Sharp general bounds are proved, in particular involving the total and the outer mutual-visibility number of base graphs. Several exact values are also determined, in particular the mutual-visibility number of the double graphs and of the Mycielskian of cycles.

Suggested Citation

  • Roy, Dhanya & Klavžar, Sandi & Lakshmanan S, Aparna, 2025. "Mutual-visibility and general position in double graphs and in Mycielskians," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    • Handle: RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324005927
    DOI: 10.1016/j.amc.2024.129131
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    References listed on IDEAS

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    1. Di Stefano, Gabriele, 2022. "Mutual visibility in graphs," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    2. 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).
    3. 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).
    4. 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.
    5. Klavžar, Sandi & Rus, Gregor, 2021. "The general position number of integer lattices," Applied Mathematics and Computation, Elsevier, vol. 390(C).
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