| Title: | On the metric subgraphs of a graph |
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| Authors: | ID Hu, Yanan (Author)
ID Zhan, Xingzhi (Author) |
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| Files: |  AMC_Hu_Yanan_Zhan_Xingzhi_2025.pdf (533,77 KB)
MD5: 4B5F4704029CE1F0DD7FAE1F1BECA81F
 https://amc-journal.eu/index.php/amc/article/view/2992
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
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| Abstract: | The three subgraphs of a connected graph induced by the center, annulus and periphery are called its metric subgraphs. The main results are as follows. (1) There exists a graph of order n whose metric subgraphs are all paths if and only if n ≥ 13 and the smallest size of such a graph of order 13 is 22; (2) there exists a graph of order n whose metric subgraphs are all cycles if and only if n ≥ 15, and there are exactly three such graphs of order 15; (3) for every integer k ≥ 3, we determine the possible orders for the existence of a graph whose metric subgraphs are all connected k-regular graphs; (4) there exists a graph of order n whose metric subgraphs are connected and pairwise isomorphic if and only if n ≥ 24 and n is divisible by 3. An unsolved problem is posed. |
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| Keywords: | center, annulus, periphery, metric subgraphs, path, cycle |
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| Publication version: | Version of Record |
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| Publication date: | 11.02.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 13 |
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| Numbering: | Vol. 25, no. 1, [article no.] P1.03 |
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| PID: | 20.500.12556/RUP-21747  |
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| ISSN: | 1855-3966 |
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| UDC: | 519.17 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.2992.a6d |
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| Publication date in RUP: | 16.09.2025 |
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| Views: | 321 |
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| Downloads: | 8 |
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