20.500.12556/DiRROS-20568 Mutual-visibility and general position in double graphs and in Mycielskians 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. general position mutual-visibility double graph Mycielskian graph outer mutual-visibility total mutual-visibility splošna lega vzajemna vidnost dvojni graf graf Mycielskega zunanja vzajemna vidnost celotna vzajemna vidnost true false true Angleški jezik Slovenski jezik Neznano 2024-10-23 07:58:53 2024-10-23 07:58:54 2024-11-06 03:34:16 0000-00-00 00:00:00 2025 0 0 Spletna objava: 17. 10. 2024; 9 str. [article no.] 129131 Vol. 488 Mar. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-03-01 519.17 0096-3003 10.1016/j.amc.2024.129131 212344835 1-s2.0-S0096300324005927-main-1.pdf 1-s2.0-S0096300324005927-main-1.pdf 1 CCF4A02E1ACFD47BE5766044C67A0A7D 3c5111ac94a23c909bf5d674d7a65c451f2a7bc8ba22976606d012fc9625ca20 40fe51c1-9104-11ef-89f3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=29018 https://www.sciencedirect.com/science/article/pii/S0096300324005927 1 e39eba65-9103-11ef-89f3-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=29017 Inštitut za matematiko, fiziko in mehaniko 0 0 0