20.500.12556/DKUM-65337 Edge-transitive lexicographic and cartesian products Povezavno-tranzitivni leksikografski in kartezični produkti In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product ▫$G \circ H$▫ of a connected graph ▫$G$▫ that is not complete by a graph ▫$H$▫, we show that it is edge-transitive if and only if ▫$G$▫ is edge-transitive and ▫$H$▫ is edgeless. If the first factor of ▫$G \circ H$▫ is non-trivial and complete, then ▫$G \circ H$▫ is edge-transitive if and only if ▫$H$▫ is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang, Xu, and Zhao (Appl. Math. Lett. 24 (2011) 1924--1926). For the Cartesian product it is shown that every connected Cartesian product of at least two non-trivial factors is edge-transitive if and only if it is the Cartesian power of a connected, edge- and vertex-transitive graph. Karakterizirani so povezani, povezavno-tranzitivni leksikografski in kartezični produkti. Za leksikografski produkt ▫$G \circ H$▫, kjer je $G$ povezan in ni poln, dokažemo, da je povezavno-tranzitiven natanko tedaj, ko je ▫$G$▫ povezavno-tranzitiven in je ▫$H$▫ brez povezav.Če je prvi faktor produkta ▫$G \circ H$▫ netrivialen in poln, potem je ▫$G\circ H$▫ povezavno-tranzitiven natanko tedaj, ko je ▫$H$▫ leksikografski produkt polnega grafa z grafom brez povezav. S tem je popravljena napaka avtorjev Li, Wang, Xu in Zhao (Appl. Math. Lett. 24 (2011) 1924--1926). Za kartezični produkt je dokazano, da je kartezični produkt vsaj dveh netrivialnih faktorjev povezavno-tranzitiven natanko tedaj, ko je kartezična potenca povezanega, povezavno- in vozliščno-tranzitivnega grafa. edge-transitive graph vertex-transitive graph lexicographic product of graphs Cartesian product of graphs povezavno-tranzitivni graf vozliščno-tranzitivni graf leksikografski produkt grafov kartezični produkt grafov true true true University of Zielona Góra Angleški jezik Slovenski jezik Znanstveno delo 2017-03-31 11:06:16 2017-03-31 11:11:42 2026-01-05 14:25:08 2019-07-11 15:15:00 2016 0 0 Str. 857-865 št. 4 Letn. 36 2016 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2015-04-16 2015-12-29 2015-12-29 1234-3099 519.17 7487065 17777241 1234-3099 URN:SI:UM:DK:HWK1G8VH Discussiones_Mathematicae_Graph_Theory_2016_Imrich_et_al._Edge-transitive_lexicographic_and_Cartesian_products.pdf Discussiones_Mathematicae_Graph_Theory_2016_Imrich_et_al._Edge-transitive_lexicographic_and_Cartesian_products.pdf 1 69CDEAAAF474E8D160D243D46BBD6A32 b61c235857b05e8f4dd2084f9147f216bdffa90d2b92af90832d0cffc618ced3 0b661a33-7c0e-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=110400 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1892 1 https://dk.um.si/Dokument.php?lang=slv&id=110401 Fakulteta za naravoslovje in matematiko 0 0 0