| Title: | Mutual-visibility and general position in double graphs and in Mycielskians |
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| Authors: | ID Roy, Dhanya (Author)
ID Klavžar, Sandi (Author)
ID Lakshmanan S., Aparna (Author) |
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| Files: |  PDF - Presentation file, download (816,77 KB)
MD5: CCF4A02E1ACFD47BE5766044C67A0A7D
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0096300324005927
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| 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. |
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| Keywords: | general position, mutual-visibility, double graph, Mycielskian graph, outer mutual-visibility, total mutual-visibility |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.03.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 9 str. |
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| Numbering: | Vol. 488, [article no.] 129131 |
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| PID: | 20.500.12556/DiRROS-20568  |
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| UDC: | 519.17 |
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| ISSN on article: | 0096-3003 |
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| DOI: | 10.1016/j.amc.2024.129131 |
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| COBISS.SI-ID: | 212344835 |
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| Note: | Spletna objava: 17. 10. 2024;
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| Publication date in DiRROS: | 23.10.2024 |
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| Views: | 119 |
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| Downloads: | 62 |
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| Metadata: |    |
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