تقرير
A note on girth-diameter cages
| العنوان: | A note on girth-diameter cages |
|---|---|
| المؤلفون: | Araujo-Pardo, Gabriela, Conder, Marston, García-Colín, Natalia, Kiss, György, Leemans, Dimitri |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C35, 51E15 |
| الوصف: | In this paper, we introduce a problem closely related to the Cage Problem and the Degree Diameter Problem. For integers $k\geq 2$, $g\geq 3$ and $d\geq 1$, we define a $(k;\, g,d)$-graph to be a $k$-regular graph with girth $g$ and diameter $d$. We denote by $n_0(k;\,g,d)$ 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 $n_0(k;\,5,4) \geq k^2+k+2$ for all $k$, and report on the determination of all $(k;\,5,4)$-cages for $k=3, 4$ and $5$ and examples with $k = 6$, and describe some examples of $(k;\,5,4)$-graphs which prove that $n_0(k;\,5,4) \leq 2k^2$ for infinitely many values of $k$. Comment: 8 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.15539 |
| رقم الأكسشن: | edsarx.2401.15539 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |