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43. Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphsPrimož Potočnik, Pablo Spiga, Gabriel Verret, 2015, original scientific article Keywords: valenca 3, valenca 4, točkovna tranzitivnost, ločna tranzitivnost, lokalno-diedrski, valency 3, valency 4, vertex-transitive, arc-transitive, locally-dihedral
Published in RUP: 15.10.2015; Views: 3019; Downloads: 201
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44. Algebraični aspekti teorije grafov : doktorska disertacijaAdemir Hujdurović, 2013, doctoral dissertation Keywords: circulant, bicirculant, semiregular automorphism, vertex-transitive graph, half-arc-transitive graph, snark, Cayley graph, quasi m-Cayley graph, generalized Cayley graph, I-regular action, regular cover of a graph, automorphism group
Published in RUP: 10.07.2015; Views: 3481; Downloads: 42
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48. 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: 2980; Downloads: 93
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49. Hamilton paths and cycles in vertex-transitive graphs of order 6pKlavdija Kutnar, Primož Šparl, 2009, original scientific article Abstract: It is shown that every connected vertex-transitive graph of order ▫$6p$▫, where ▫$p$▫ is a prime, contains a Hamilton path. Moreover, it is shown that, except for the truncation of the Petersen graph, every connected vertex-transitive graph of order ▫$6p$▫ which is not genuinely imprimitive contains a Hamilton cycle.
Keywords: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Published in RUP: 15.10.2013; Views: 3445; Downloads: 40
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