Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 10 1 2025 03 01 On the distance-transitivity of the folded hypercube 207 217 14656 10.22049/cco.2023.28704.1679 EN Seyed Morteza Mirafzal Department of Mathematics, Faculty of Basic Science, Lorestan University, Khorramabad, Iran Journal Article 2023 06 01 The folded hypercube $FQ_n$ is the Cayley graph Cay$(\mathbb{Z}_2^n,S)$, where $S=\{e_1,e_2,\dots,e_n\}\cup <br />\{u=e_1+e_2+\dots+e_n\}$, 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. https://comb-opt.azaruniv.ac.ir/article_14656_78491c62c325cd731571e4541bce6a62.pdf