1. The automorphism groups of non-edge transitive rose window graphsEdward Dobson, István Kovács, Štefko Miklavič, 2015, original scientific article Abstract: In this paper, we determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we determine the isomorphism classes of non-edge-transitive rose window graphs. Keywords: rose window graphs, automorphism group, isomorphism problem, vertex-transitive graph Published in RUP: 31.12.2021; Views: 879; Downloads: 18 Full text (275,74 KB) |
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3. Classification of edge-transitive rose window graphsIstván Kovács, Klavdija Kutnar, Dragan Marušič, 2010, original scientific article Abstract: Given natural numbers ▫$n \ge 3$▫ and ▫$1 \le a$▫, ▫$r \le n-1$▫, the rose window graph ▫$R_n(a,r)$▫ is a quartic graph with vertex set ▫$\{x_i \vert i \in {\mathbb Z}_n\} \cup \{y_i \vert i \in {\mathbb Z}_n\}$▫ and edge set ▫$\{\{x_i, x_{i+1}\} \vert i \in {\mathbb Z}_n\} \cup \{\{y_i, y_{i+r}\} \vert i \in {\mathbb Z}_n\} \cup \{\{x_i, y_i\} \vert i \in {\mathbb Z}_n\} \cup \{\{x_{i+a}, y_i\} \vert i \in {\mathbb Z}_n\}$▫. In this article a complete classification of edge-transitive rose window graphs is given, thus solving one of three open problems about these graphs posed by Steve Wilson in 2001. Keywords: group, graph, rose window, vertex-transitive, edge-transitive, arc-transitive Published in RUP: 15.10.2013; Views: 2899; Downloads: 92 Link to full text |
4. Characterization of edge-transitive 4-valent bicirculantsIstván Kovács, Boštjan Kuzman, Aleksander Malnič, Steve Wilson, 2012, original scientific article Abstract: Bicirkulant je graf, ki dopušča avtomorfizem z natanko dvema orbitama vozlišč enake velikosti. V članku so karakterizirani vsi neizomorfni 4-valentni povezavno tranzitivni bicirkulanti. Posledično je izpeljana karakterizacija 4-valentnih ločno tranzitivnih dihedrantov. Keywords: matematika, teorija grafov, štirivalenten graf, bicirkulantni graf, Cayleyev graf, povezavno tranzitiven graf, ločno tranzitiven graf, dihedrant, rose window graf, grupa avtomorfizmov Published in RUP: 15.10.2013; Views: 3799; Downloads: 146 Link to full text |