20.500.12556/RUP-23172 Classification of pentavalent symmetric tricirculants A graph $\Gamma$ is said to be an {\em $m$-Cayley graph} on a group $G$ ($|G|\ne 1$) if its automorphism group contains a semiregular subgroup isomorphic to $G$ having $m$ orbits on the vertex set of $\Gamma$. If $G$ is cyclic and $m=3$ then $\Gamma$ is called a {\em tricirculant}. A graph is said to be {\em symmetric} if its automorphism group acts transitively on the set of its arcs. In this paper, it is shown that with the exception of $K_6$, no connected pentavalent symmetric tricirculant exists. Grafu $\Gamma$ pravimo {\em $m$-Cayleyjev graf} grupe $G$ ($|G|\ne 1$), če njegova grupa avtomorfizmov vsebuje polregularno podgrupo, izomorfno grupi $G$, ki ima $m$ orbit na množici točk grafa $\Gamma$. Če je $G$ ciklična grupa in $m=3$, potem $\Gamma$ imenujemo {\em tricirkulant}. Grafu pravimo {\em simetričen}, če njegova grupa avtomorfizmov deluje tranzitivno na množici njegovih lokov. V tem članku je pokazano, da z izjemo $K_6$ ne obstaja noben povezan petvalenten simetričen tricirkulant. pentavalent graph symmetric semiregular automorphism tricirculant petvalentni graf simetrični polregularni avtomorfizem tricirkulant true false true Angleški jezik Slovenski jezik Članek v reviji 2026-06-22 08:35:11 2026-06-22 08:35:13 2026-06-23 03:05:43 0000-00-00 00:00:00 2026 0 0 str. 1-20 no. Vol. 2026 0000-00-00 PostprintKoncna NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2026-06-19 519.17 1855-3974 10.26493/1855-3974.3588.9fb 282366467 RAZ_Khaefi_Yasamin_2026.pdf RAZ_Khaefi_Yasamin_2026.pdf 1 FAC3334B4B4B959A32CB2B61E5A816A5 4bef2f16745fd34aedfe5452d336fe997a8acc49400f77f74d292be1fc2a4e29 a4670996-6e04-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33868 https://amc-journal.eu/index.php/amc/article/view/3588 1 5ef68ffa-6e04-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33867 Univerza na Primorskem 0 0 0