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On the distance-transitivity of the folded hypercube | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 آبان 1402 اصل مقاله (441.91 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28704.1679 | ||
| نویسنده | ||
| Seyed Morteza Mirafzal* | ||
| Lorestan university | ||
| چکیده | ||
| The folded hypercube $FQ_n$ is the Cayley graph Cay$(\mathbb{Z}_2^n,S)$, where $S=\{e_1,e_2,\dots,e_n\}\cup \{u=e_1+e_2+\dots+e_n\}$, and $e_i = (0,\dots, 0, 1, 0,$ $\dots, 0)$, with 1 at the $i$th position, $1\leq i \leq n$. In this paper, we show that the folded hypercube $FQ_n$ is a distance-transitive graph. Then, we study some properties of this graph. In particular, we show that if $n\geq 4$ is an even integer, then the folded hypercube $FQ_n$ is an $automorphic$ graph, that is, $FQ_n$ is a distance-transitive primitive graph which is not a complete or a line graph. | ||
| کلیدواژه‌ها | ||
| Distance-transitive graph؛ folded hypercube؛ distance regular graph؛ primitive graph؛ automorphic graph | ||
| مراجع | ||
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