Automorphism group of a family of distance-regular graphs which are not distance-transitive

Mirafzal, Seyed Morteza; Das, Angsuman

doi:10.22108/toc.2025.142386.2200

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	Automorphism group of a family of distance-regular graphs which are not distance-transitive
Transactions on Combinatorics
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نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.142386.2200
نویسندگان
Seyed Morteza Mirafzal^* ¹؛ Angsuman Das²
¹Department of Mathematics, Lorestan University, Khorramabad, Iran
²Department of Mathematics, Presidency University, Kolkata, India
چکیده
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.
کلیدواژه‌ها
strongly regular graph؛ distance-transitive graph؛ graph automorphism؛ clique

مراجع
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Automorphism group of a family of distance-regular graphs which are not distance-transitive