Abstract
Abstract A map is called edge-regular if it is edge-transitive but not arc-transitive. In this paper, we show that a complete graph K n {K}_{n} has an orientable edge-regular embedding if and only if n = p d > 3 n={p}^{d}\gt 3 with p an odd prime such that p d ≡ 3 {p}^{d}\equiv 3 ( mod 4 ) (\mathrm{mod}\hspace{.25em}4) . Furthermore, K p d {K}_{{p}^{d}} has p d − 3 4 d ϕ ( p d − 1 2 ) \tfrac{{p}^{d}-3}{4d}\hspace{0.25em}\phi \left(\tfrac{{p}^{d}-1}{2}\right) non-isomorphic orientable edge-regular embeddings.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.