Abstract
Murty [A generalization of the Hoffman–Singleton graph, Ars Combin. 7 (1979) 191–193.] constructed a family of ( p m + 2 ) -regular graphs of girth five and order 2 p 2 m , where p ⩾ 5 is a prime, which includes the Hoffman–Singleton graph [A.J. Hoffman, R.R. Singleton, On Moore graphs with diameters 2 and 3, IBM J. (1960) 497–504]. This construction gives an upper bound for the least number f ( k ) of vertices of a k-regular graph with girth 5. In this paper, we extend the Murty construction to k-regular graphs with girth 5, for each k. In particular, we obtain new upper bounds for f ( k ) , k ⩾ 16 .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
