# Iskanje po repozitoriju

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 1 - 10 / 30123 1.Hamilton paths in vertex-transitive graphs of order 10pKlavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, izvirni znanstveni članekOpis: It is shown that every connected vertex-transitive graph of order ▫$10p$▫, ▫$p \ne 7$▫ a prime, which is not isomorphic to a quasiprimitive graph arising from the action of PSL▫$(2,k)$▫ on cosets of ▫$\mathbb{Z}_k \times \mathbb{Z}_{(k-1)/10}$▫, contains a Hamilton path.Najdeno v: ključnih besedahKljučne besede: graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism groupObjavljeno: 15.10.2013; Ogledov: 1905; Prenosov: 12 Polno besedilo (0,00 KB) 2.On the order of arc-stabilisers in arc-transitive graphs, IIGabriel Verret, 2013, izvirni znanstveni članekNajdeno v: ključnih besedahPovzetek najdenega: ...arc-transitive graphs, graph-restrictive group, local action, ...Ključne besede: arc-transitive graphs, graph-restrictive group, local actionObjavljeno: 15.10.2013; Ogledov: 2170; Prenosov: 52 Polno besedilo (0,00 KB) 3.Hamiltonicity of vertex-transitive graphs of order 4pKlavdija Kutnar, Dragan Marušič, 2008, izvirni znanstveni članekOpis: It is shown that every connected vertex-transitive graph of order ▫$4p$▫, where ▫$p$▫ is a prime, is hamiltonian with the exception of the Coxeter graph which is known to possess a Hamilton path.Najdeno v: ključnih besedahKljučne besede: graph theory, vertex-transitive graphs, Hamilton cycle, automorphism groupObjavljeno: 15.10.2013; Ogledov: 1797; Prenosov: 18 Polno besedilo (0,00 KB) 4.Classification of 2-arc-transitive dihedrantsShao Fei Du, Aleksander Malnič, Dragan Marušič, 2008, izvirni znanstveni članekOpis: A complete classification of 2-arc-transitive dihedrants, that is, Cayley graphs of dihedral groups is given, thus completing the study of these graphs initiated by the third author in [D. Marušič, On 2-arc-transitivity of Cayley graphs, J. Combin. Theory Ser. B 87 (2003) 162-196]. The list consists of the following graphs: (i) cycles ▫$C_{2n},\; n \ge 3$▫; (ii) complete graphs ▫$K_{2n}, \; n \ge 3$▫; (iii) complete bipartite graphs ▫$K_{n,n}, \; n \ge 3$▫; (iv) complete bipartite graphs minus a matching ▫$K_{n,n} - nK_2, \; n \ge 3$▫; (v) incidence and nonincidence graphs ▫$B(H_{11})$▫ and ▫$B'(H_{11})$▫ of the Hadamard design on 11 points; (vi) incidence and nonincidence graphs ▫$B(PG(d,q))$▫ and ▫$B'(PG(d,q))$▫, with ▫$d \ge 2$▫ and ▫$q$▫ a prime power, of projective spaces; (vii) and an infinite family of regular ▫${\mathbb{Z}}_d$▫-covers ▫$K_{q+1}^{2d}$▫ of ▫$K_{q+1, q+1} - (q+1)K_2$▫, where ▫$q \ge 3$▫ is an odd prime power and ▫$d$▫ is a divisor of ▫$\frac{q-1}{2}$▫ and ▫$q-1$▫, respectively, depending on whether ▫$q \equiv 1 \pmod{4}$▫ or ▫$q \equiv 3 \pmod{4}$▫ obtained by identifying the vertex set of the base graph with two copies of the projective line ▫$PG(1,q)$▫, where the missing matching consists of all pairs of the form ▫$[i,i']$▫, ▫$i \in PG(1,q)$▫, and the edge ▫$[i,j']$▫ carries trivial voltage if ▫$i=\infty$▫ or ▫$j=\infty$▫, and carries voltage ▫$\bar{h} \in {\mathbb{Z}}_d$▫, the residue class of ▫$h \in {\mathbb{Z}}_d$▫, if and only if ▫$i-j = \theta^h$▫, where ▫$\theta$▫ generates the multiplicative group ▫${\mathbb{F}}_q^\ast$▫ of the Galois field ▫${\mathbb{F}}_q$▫.Najdeno v: ključnih besedahPovzetek najdenega: ...dihedrants, that is, Cayley graphs of dihedral groups is given, thus completing the study of...Ključne besede: permutation group, imprimitive group, dihedral group, Cayley graph, dihedrant, 2-Arc-transitive graphObjavljeno: 15.10.2013; Ogledov: 1751; Prenosov: 56 Polno besedilo (0,00 KB) 5.On quartic half-arc-transitive metacirculantsDragan Marušič, Primož Šparl, 2008, izvirni znanstveni članekOpis: Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ▫$\rho$▫ and ▫$\sigma$▫, where ▫$\rho$▫ is ▫$(m,n)$▫-semiregular for some integers ▫$m \ge 1$▫, ▫$n \ge 2▫$, and where ▫$\sigma$▫ normalizes ▫$\rho$▫, cyclically permuting the orbits of ▫$\rho$▫ in such a way that ▫$\sigma^m$▫ has at least one fixed vertex. A half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In this article quartic half-arc-transitive metacirculants are explored and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic half-arc-transitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed.Najdeno v: ključnih besedahPovzetek najdenega: ...graph is a graph admitting a transitive group generated by two automorphisms ▫$\rho$▫ and ▫$\sigma$▫,...Ključne besede: mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism groupObjavljeno: 15.10.2013; Ogledov: 1845; Prenosov: 75 Polno besedilo (0,00 KB) 6.Distance-regular Cayley graphs on dihedral groupsŠtefko Miklavič, Primož Potočnik, 2007, izvirni znanstveni članekOpis: The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every non-trivial distance-regular Cayley graph on a dihedral group is bipartite, non-antipodal, has diameter 3 and arises either from a cyclic di#erence set, or possibly (if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all distance-transitive Cayley graphs on dihedral groups are determined. It transpires that a Cayley graph on a dihedral group is distance-transitive if and only if it is trivial, or isomorphic to the incidence or to the non-incidence graph of a projective space ▫$\mathrm{PG}_{d-1} (d,q)$▫, ▫$d \ge 2$▫, or the unique pair of complementary symmetric designs on 11 vertices.Najdeno v: ključnih besedahPovzetek najdenega: ...set satisfying some additional conditions. Finally, all distance- transitive Cayley graphs on dihedral groups are determined.... ...classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such...Ključne besede: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference setObjavljeno: 15.10.2013; Ogledov: 1395; Prenosov: 64 Polno besedilo (0,00 KB) 7.Hamilton paths and cycles in vertex-transitive graphs of order 6pKlavdija Kutnar, Primož Šparl, 2009, izvirni znanstveni članekOpis: 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.Najdeno v: ključnih besedahKljučne besede: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism groupObjavljeno: 15.10.2013; Ogledov: 1847; Prenosov: 14 Polno besedilo (0,00 KB) 8.Classification of edge-transitive rose window graphsIstván Kovács, Klavdija Kutnar, Dragan Marušič, 2010, izvirni znanstveni članekOpis: 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.Najdeno v: ključnih besedahPovzetek najdenega: ... group, graph, rose window, vertex-transitive, edge-transitive, arc-transitive...Ključne besede: group, graph, rose window, vertex-transitive, edge-transitive, arc-transitiveObjavljeno: 15.10.2013; Ogledov: 1441; Prenosov: 57 Polno besedilo (0,00 KB) 9.On cubic non-Cayley vertex-transitive graphsKlavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, izvirni znanstveni članekNajdeno v: ključnih besedahPovzetek najdenega: ...vertex-transitive graph, non-Cayley graph, automorphism group, ...Ključne besede: vertex-transitive graph, non-Cayley graph, automorphism groupObjavljeno: 15.10.2013; Ogledov: 1434; Prenosov: 72 Polno besedilo (0,00 KB) 10.Hamilton cycles in (2, odd, 3)-Cayley graphsHenry Glover, Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, 2012, izvirni znanstveni članekOpis: In 1969, Lovász asked if every finite, connected vertex-transitive graph has a Hamilton path. In spite of its easy formulation, no major breakthrough has been achieved thus far, and the problem is now commonly accepted to be very hard. The same holds for the special subclass of Cayley graphs where the existence of Hamilton cycles has been conjectured. In 2007, Glover and Marušič proved that a cubic Cayley graph on a finite ▫$(2, s, 3)$▫-generated group ▫$G = \langle a, x| a^2 = x^s = (ax)^3 = 1, \dots \rangle$▫ has a Hamilton path when ▫$|G|$▫ is congruent to 0 modulo 4, and has a Hamilton cycle when ▫$|G|$▫ is congruent to 2 modulo 4. The Hamilton cycle was constructed, combining the theory of Cayley maps with classical results on cyclic stability in cubic graphs, as the contractible boundary of a tree of faces in the corresponding Cayley map. With a generalization of these methods, Glover, Kutnar and Marušič in 2009 resolved the case when, apart from ▫$|G|$▫, also ▫$s$▫ is congruent to 0 modulo 4. In this article, with a further extension of the above "tree of faces" approach, a Hamilton cycle is shown to exist whenever ▫$|G|$▫ is congruent to 0 modulo 4 and s is odd. This leaves ▫$|G|$▫ congruent to 0 modulo 4 with s congruent to 2 modulo 4 as the only remaining open case. In this last case, however, the "tree of faces" approach cannot be applied, and so entirely different techniques will have to be introduced if one is to complete the proof of the existence of Hamilton cycles in cubic Cayley graphs arising from finite ▫$(2, s, 3)$▫-generated groups.Najdeno v: ključnih besedahPovzetek najdenega: ...1969, Lovász asked if every finite, connected vertex- transitive graph has a Hamilton path. In spite... ...graph on a finite ▫$(2, s, 3)$▫-generated group ▫\$G = \langle a, x| a^2 =...Ključne besede: Cayley graph, Hamilton cycle, arc-transitive graph, 1-regular action, automorphism groupObjavljeno: 15.10.2013; Ogledov: 1356; Prenosov: 69 Polno besedilo (0,00 KB)
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