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https://research.matf.bg.ac.rs/handle/123456789/1334| Title: | On the order of antipodal covers | Authors: | Wang, Jianfeng Zhang, Wenqian Wang, Yiqiao Stanić, Zoran |
Keywords: | antipodal cover;diameter;distance-regular graph;fibre | Issue Date: | 1-Feb-2024 | Rank: | M22 | Publisher: | Wiley | Journal: | Journal of Graph Theory | Abstract: | A noncomplete graph (Formula presented.) of diameter (Formula presented.) is called an antipodal (Formula presented.) -cover if its vertex set can be partitioned into the subsets (also called fibres) (Formula presented.) of (Formula presented.) vertices each, in such a way that two vertices of (Formula presented.) are at distance (Formula presented.) if and only if they belong to the same fibre. We say that (Formula presented.) is symmetric if for every (Formula presented.), there exist (Formula presented.) such that (Formula presented.), where (Formula presented.). In this paper, we prove that, for (Formula presented.), an antipodal (Formula presented.) -cover which is not a cycle, has at least (Formula presented.) vertices provided (Formula presented.), and at least (Formula presented.) vertices provided it is symmetric. Our results extend those of Göbel and Veldman. |
Description: | This is the peer reviewed version of the following article: J. Wang, W. Zhang, Y. Wang and Z. Stanić, On the order of antipodal covers, J. Graph Theory. 2024; 105: 285–296. https://doi.org/10.1002/jgt.23037, which has been published in final form at https://doi.org/10.1002/jgt.23037. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited. |
URI: | https://research.matf.bg.ac.rs/handle/123456789/1334 | ISSN: | 03649024 | DOI: | 10.1002/jgt.23037 |
| Appears in Collections: | Research outputs |
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