Affiliation:
1. School of Mathematics and Statistics Shandong University of Technology Zibo China
2. Faculty of Science Beijing University of Technology Beijing China
3. Faculty of Mathematics University of Belgrade Belgrade Serbia
Abstract
AbstractA 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.
Subject
Geometry and Topology,Discrete Mathematics and Combinatorics
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