| Title: | A note on girth-diameter cages |
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| Authors: | ID Araujo-Pardo, Gabriela (Author)
ID Conder, Marston D. E. (Author)
ID García-Colín, Natalia (Author)
ID Kiss, György (Author)
ID Leemans, Dimitri (Author) |
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| Files: |  RAZ_Araujo-Pardo_Gabriela_2025.pdf (378,53 KB)
MD5: BA99B645FB067A06FEB7BCAFE2CA23B6
 https://adam-journal.eu/index.php/ADAM/article/view/1743
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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: | In this paper we introduce a problem closely related to the Cage Problem and the Degree Diameter Problem. For integers k ≥ 2, g ≥ 3 and d ≥ 1, we define a (k; g, d)-graph to be a k-regular graph with girth g and diameter d. We denote by n₀(k; g, d) the smallest possible order of such a graph, and, if such a graph exists, we call it a (k; g, d)-cage. In particular, we focus on (k; 5, 4)-graphs. We show that n₀(k; 5, 4) ≥ k² + k + 2 for all k, and report on the determination of all (k; 5, 4)-cages for k = 3, 4 and 5 and of examples with k = 6, and describe some examples of (k; 5, 4)-graphs which prove that n₀(k; 5, 4) ≤ 2k² for infinitely many k. |
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| Keywords: | cages, girth, degree-diameter problem |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 09.06.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1-7 |
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| Numbering: | Vol. 8, no. 3, [article no.] P3.06 |
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| PID: | 20.500.12556/RUP-21342  |
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| UDC: | 519.17 |
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| ISSN on article: | 2590-9770 |
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| DOI: | 10.26493/2590-9770.1743.19f |
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| COBISS.SI-ID: | 238839043 |
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| Publication date in RUP: | 10.06.2025 |
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| Views: | 666 |
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| Downloads: | 15 |
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| Metadata: |    |
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