تقرير
Automorphism group of a family of distance regular graphs which are not distance transitive
| العنوان: | Automorphism group of a family of distance regular graphs which are not distance transitive |
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| المؤلفون: | Das, Angsuman, Mirafzal, S. Morteza |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C25 |
| الوصف: | Let $G_n=\mathbb{Z}_n\times \mathbb{Z}_n$ for $n\geq 4$ and $S=\{(i,0),(0,i),(i,i): 1\leq i \leq n-1\}\subset G_n$. Define $\Gamma(n)$ to be the Cayley graph of $G_n$ with respect to the connecting set $S$. It is known that $\Gamma(n)$ is a strongly regular graph with the parameters $(n^2,3n-3,n,6)$ \cite{19}. Hence $\Gamma(n)$ is a distance regular graph. It is known that every distance transitive graph is distance regular, but the converse is not true. In this paper, we study some algebraic properties of the graph $\Gamma(n)$. Then by determining the automorphism group of this family of graphs, we show that the graphs under study are not distance transitive. Comment: 11 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.01293 |
| رقم الأكسشن: | edsarx.2403.01293 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |