| Title: | A note on girth-diameter cages |
|---|
| 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) |
|---|
| Files: |  RAZ_Araujo-Pardo_Gabriela_2025.pdf (378,53 KB)
MD5: BA99B645FB067A06FEB7BCAFE2CA23B6
 https://adam-journal.eu/index.php/ADAM/article/view/1743
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
|
|---|
| 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. |
|---|
| Keywords: | cages, girth, degree-diameter problem |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 09.06.2025 |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | str. 1-7 |
|---|
| Numbering: | Vol. 8, no. 3, [article no.] P3.06 |
|---|
| PID: | 20.500.12556/RUP-21342  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 2590-9770 |
|---|
| DOI: | 10.26493/2590-9770.1743.19f |
|---|
| COBISS.SI-ID: | 238839043 |
|---|
| Publication date in RUP: | 10.06.2025 |
|---|
| Views: | 89 |
|---|
| Downloads: | 3 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
