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

Dhanya Roy, Sandi Klavžar and Aparna Lakshmanan S

Applied Mathematics and Computation, 2025, vol. 488, issue C

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.

Keywords: General position; Mutual-visibility; Double graph; Mycielskian graph; Outer mutual-visibility; Total mutual-visibility (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324005927

DOI: 10.1016/j.amc.2024.129131

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