20.500.12556/RUL-171239 Edge-transitive cubic graphs: analysis, cataloguing and enumeration This paper deals with finite cubic (3-regular) graphs whose automorphism group acts transitively on the edges of the graph. Such graphs split into two broad classes, namely arc-transitive and semisymmetric cubic graphs, and then these divide respectively into 7 types (according to a classification by Djoković and Miller (1980) [17]) and 15 types (according to a classification by Goldschmidt (1980) [23]), in terms of certain group amalgams. Such graphs of small order were previously known up to orders 2048 and 768, respectively, and we have extended each of the two lists of all such graphs up to order 10000. Before describing how we did that, we carry out an analysis of the 22 amalgams, to show which of the finitely-presented groups associated with the 15 Goldschmidt amalgams can be faithfully embedded in one or more of the other 21 (as subgroups of finite index), complementing what is already known about such embeddings of the 7 Djoković-Miller groups in each other. We also give an example of a graph of each of the 22 types, and in most cases, describe the smallest such graph, and we then use regular coverings to prove that there are infinitely many examples of each type. Finally, we discuss the asymptotic enumeration of the graph orders, proving that if $f_{\mathcal C}(n)$ is the number of cubic edge-transitive graphs of type ${\mathcal C}$ on at most $n$ vertices, then there exist positive real constants $a$ and $b$ and a positive integer $n_0$ such that $n^{a \log(n)} \le f_{\mathcal C}(n) \le n^{b \log(n)}$ for all $n\ge 0$. groups graphs symmetry amalgams cover true false true Angleški jezik Angleški jezik Članek v reviji 2025-08-21 08:02:43 2025-08-21 08:02:50 2025-08-22 04:12:46 0000-00-00 00:00:00 2026 0 0 Str. 703-737 Vol. 685 Jan. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-01 519.17 0021-8693 10.1016/j.jalgebra.2025.07.035 246127363 1-s2.0-S002186932500448X-main.pdf 1-s2.0-S002186932500448X-main.pdf 1 7D7D425647CA15EB79DD83A24AC868C1 7bf34060d473b9d21fa113b4e956509c8958c786b2e9396f7fbe6e55a1f32517 b6474481-7e54-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=214430 https://www.sciencedirect.com/science/article/pii/S002186932500448X 1 5dcd8db1-7e54-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=214429 Fakulteta za matematiko in fiziko 0 0 0