تقرير
Semicubic cages and small graphs of even girth from voltage graphs
| العنوان: | Semicubic cages and small graphs of even girth from voltage graphs |
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| المؤلفون: | Aguilar, Flor, Araujo-Pardo, Gabriela, Bermann, Leah |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C35 |
| الوصف: | An \emph{$(3,m;g)$ semicubic graph} is a graph in which all vertices have degrees either $3$ or $m$ and fixed girth $g$. In this paper, we construct families of semicubic graphs of even girth and small order using two different techniques. The first technique generalizes a previous construction which glues cubic cages of girth $g$ together at remote vertices (vertices at distance at least $g/2$). The second technique, the main content of this paper, produces bipartite semicubic $(3,m; g)$-graphs with fixed even girth $g = 4t$ or $4t+2$ using voltage graphs over $\mathbb{Z}_{m}$. When $g = 4t+2$, the graphs have two vertices of degree $m$, while when $g = 4t$ they have exactly three vertices of degree $m$ (the remaining vertices are of degree $3$ in both cases). Specifically, we describe infinite families of semicubic graphs $(3,m; g)$ for $g = \{6, 8, 10, 12\}$ for infinitely many values of $m$. The cases $g = \{6,8\}$ include the unique $6$-cage and the unique $8$-cage when $m = 3$. The families obtained in this paper for girth $g=\{10,12\}$ include examples with the best known bounds for semicubic graphs $(3,m; g)$ Comment: 28 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.03290 |
| رقم الأكسشن: | edsarx.2305.03290 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |