20.500.12556/RUP-23502 On the BCI problem O BCI problemu Let G be a group. The BCI problem asks whether two Haar graphs of G are isomorphic if and only if they are isomorphic by an element of an explicit list of isomorphisms. We first generalize this problem in a natural way and give a theoretical way to solve the isomorphism problem for the natural generalization. We then restrict our attention to abelian groups and, with an exception, reduce the problem to the isomorphism problem for a related quotient, component, or corresponding Cayley digraph. For Haar graphs of an abelian group of odd order with connection sets S those of Cayley graphs (i.e. S = -S), the exception does not exist. For Haar graphs of cyclic groups of odd order with connection sets those of a Cayley graph, among others, we solve the isomorphism problem. Naj bo G grupa. Problem BCI sprašuje, ali sta dva Haarova grafa grupe G izomorfna natanko tedaj, ko sta izomorfna prek elementa iz eksplicitno podanega seznama izomor- fizmov. Najprej ta problem na naraven naˇcin posplošimo in podamo teoretiˇcen pristop za reševanje problema izomorfizma za tako dobljeno posplošitev. Nato se omejimo na abelove grupe in z eno izjemo problem reduciramo na problem izomorfizma ustreznega kvocienta, komponente ali pripadajoˇcega Cayleyjevega digrafa. Pri Haarovih grafih abelove grupe li- hega reda s povezovalnimi množicami S, ki so povezovalne množice Cayleyjevih grafov (torej S = −S), te izjeme ni. Med drugim rešimo problem izomorfizma za Haarove grafe cikliˇcnih grup lihega reda s povezovalnimi množicami, ki ustrezajo Cayleyjevim grafom. Cayley Haar CI BCI abelian group Cayley Haar CI BCI abelova grupa true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2026-08-17 10:48:59 2026-08-17 10:48:59 2026-08-18 03:07:46 0000-00-00 00:00:00 2026 0 0 29 str. no. 3, [article no.] P3.01 Vol. 26 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-05-19 51 1855-3974 10.26493/1855-3974.3490.91f AMC_Dobson,_Robson_2026.pdf AMC_Dobson,_Robson_2026.pdf 1 BBA39FAC26B872F4E857BF4679A11258 c9eb0dbfd271b1d105ea48f04cbd0157ad2f2e9b9c126b246fba1b9087f1a522 301c7c28-9a19-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=34493 Založba Univerze na Primorskem 0 0 0