On the order of antipodal covers
Jianfeng Wang, Wenqian Zhang, Yiqiao Wang, Zoran Stanić · Journal of Graph Theory · 2023
Abstract A noncomplete graph of diameter is called an antipodal ‐cover if its vertex set can be partitioned into the subsets (also called fibres) of vertices each, in such a way that two vertices of are at distance if and only if they belong to the same fibre. We say that is symmetric if for every , there exist such that , where . In this paper, we prove that, for , an antipodal ‐cover which is not a cycle, has at least vertices provided , and at least vertices provided it is symmetric. Our results extend those of Göbel and Veldman.