{"pk":65042,"title":"The intersection density of cubic arc-transitive graphs with \\(2\\)-arc-regular full automorphism group equal to \\( \\operatorname{PGL}_{2}(q)\\)","subtitle":null,"abstract":"The intersection density of a transitive permutation group \\(G\\leq \\operatorname{Sym}(V)\\) is the ratio between the largest size of a subset of \\(G\\) in which any two agree on at least one element of \\(V\\), and the order of a point-stabilizer of \\(G\\). In this paper, we determine the intersection densities of the automorphism groups of the arc-transitive graphs admitting a \\(2\\)-arc-regular full automorphism group \\(G^* = \\operatorname{PGL}_{2}(q)\\) and an arc-regular subgroup of automorphism \\(G = \\operatorname{PSL}_{2}(q)\\).\n \nMathematics Subject Classifications: 05C35, 05C69, 20B05\n \nKeywords: Derangement graphs, cocliques, projective special linear groups","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Derangement graphs"},{"word":"cocliques"},{"word":"projective special linear groups"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/8pf69809","frozenauthors":[{"first_name":"Karen","middle_name":"","last_name":"Meagher","name_suffix":"","institution":"Department of Mathematics and Statistics, University of Regina, Regina, SK, S4S 0A2, Canada","department":""},{"first_name":"Andriaherimanana","middle_name":"Sarobidy","last_name":"Razafimahatratra","name_suffix":"","institution":"Fields Institute for Research in Mathematical Sciences, 222 College St, Toronto, Canada","department":""}],"date_submitted":"2026-04-20T19:45:16Z","date_accepted":"2026-04-20T19:45:16Z","date_published":"2026-04-20T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/65042/galley/49852/download/"}]}