Abstract
Let GP (q2,m) be the m-Paley graph defined on the finite field with order q2. We study eigenfunctions and maximal cliques in generalised Paley graphs GP (q2,m), where m|(q+1). In particular, we explicitly construct maximal cliques of size q+1m or q+1m+1 in GP (q2,m), and show the weight-distribution bound on the cardinality of the support of an eigenfunction is tight for the smallest eigenvalue −q+1m of GP (q2,m). These new results extend the work of Baker et al. and Goryainov et al. on Paley graphs of square order. We also study the stability of the Erdős-Ko-Rado theorem for GP (q2,m) (first proved by Sziklai).
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.
