Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/159972
Title: Augmenting the Delsarte bound: a forbidden interval for the order of maximal cliques in strongly regular graphs
Authors: Greaves, Gary Royden Watson
Koolen, Jack H.
Park, Jongyook
Keywords: Science::Mathematics
Issue Date: 2021
Source: Greaves, G. R. W., Koolen, J. H. & Park, J. (2021). Augmenting the Delsarte bound: a forbidden interval for the order of maximal cliques in strongly regular graphs. European Journal of Combinatorics, 97, 103384-. https://dx.doi.org/10.1016/j.ejc.2021.103384
Project: RG29/18
RG21/20
Journal: European Journal of Combinatorics
Abstract: In this paper, we study the order of a maximal clique in an amply regular graph with a fixed smallest eigenvalue by considering a vertex that is adjacent to some (but not all) vertices of the maximal clique. As a consequence, we show that if a strongly regular graph contains a Delsarte clique, then the parameter μ is either small or large. Furthermore, we obtain a cubic polynomial that assures that a maximal clique in an amply regular graph is either small or large (under certain assumptions). Combining this cubic polynomial with the claw-bound, we rule out an infinite family of feasible parameters (v, k, λ, μ) for strongly regular graphs. Lastly, we provide tables of parameters (v, k, λ, μ) for nonexistent strongly regular graphs with smallest eigenvalue −4, −5, −6 or −7.
URI: https://hdl.handle.net/10356/159972
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2021.103384
Schools: School of Physical and Mathematical Sciences 
Rights: © 2021 Elsevier Ltd. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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