0 KB298 KB26 KB200820252013Devillers, AliceJin, WeiLi, Cai HengPraeger, Cheryl E.številka:1letnik:6str. 13-30COBISSID:16467289ISSN:1855-3966URN:URN:NBN:SI:doc-K3LVMJCXenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporanealine graphss-arc transitive graphss-geodesic transitive graphsLine graphs and geodesic transitivity|For a graph ?$\Gamma$?, a positive integer ?$s$? and a subgroup ?$G \le \text{Aut}(\Gamma)$?, we prove that ?$G$? is transitive on the set of ?$s$?-arcs of ?$\Gamma$? if and only if ?$\Gamma$? has girth at least ?$2(s - 1)$? and ?$G$? is transitive on the set of ?$(s - 1)$?-geodesics of its line graph. As applications, we first classify 2-geodesic transitive graphs of valency 4 and girth 3, and determine which of them are geodesic transitive. Secondly we prove that the only non-complete locally cyclic 2-geodesic transitive graphs are the octahedron and the icosahedronTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije