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1.
Hamilton paths in vertex-transitive graphs of order 10p
Klavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, original scientific article

Abstract: 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.
Found in: ključnih besedah
Keywords: graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Published: 15.10.2013; Views: 1695; Downloads: 11
URL Full text (0,00 KB)

2.
On the order of arc-stabilisers in arc-transitive graphs, II
Gabriel Verret, 2013, original scientific article

Found in: ključnih besedah
Summary of found: ...arc-transitive graphs, graph-restrictive group, local action, ...
Keywords: arc-transitive graphs, graph-restrictive group, local action
Published: 15.10.2013; Views: 1964; Downloads: 42
URL Full text (0,00 KB)

3.
Hamiltonicity of vertex-transitive graphs of order 4p
Klavdija Kutnar, Dragan Marušič, 2008, original scientific article

Abstract: 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.
Found in: ključnih besedah
Keywords: graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group
Published: 15.10.2013; Views: 1580; Downloads: 17
URL Full text (0,00 KB)

4.
The full automorphism group of Cayley graphs of ${mathbb Z}_ptimes{mathbbZ}_{p^2}$
Edward Dobson, 2012, original scientific article

Found in: ključnih besedah
Keywords: Cayley graph, abelian group, automorphism group
Published: 15.10.2013; Views: 1740; Downloads: 31
URL Full text (0,00 KB)

5.
On non-normal arc-transitive 4-valent dihedrants
István Kovács, Boštjan Kuzman, Aleksander Malnič, 2010, original scientific article

Abstract: Let ▫$X$▫ be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group ▫$D_n$▫ such that ▫$X$▫ is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within ▫$D_n$▫. It is shown that ▫$X$▫ is isomorphic either to the lexicographic product ▫$C_n[2K_1]$▫ with ▫$n \geq 4$▫ even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.
Found in: ključnih besedah
Summary of found: ...4-valent arc-transitive Cayley graph on a dihedral group ▫$D_n$▫ such that ▫$X$▫ is bipartite, with...
Keywords: Cayley graph, arc transitivity, dihedral group
Published: 15.10.2013; Views: 1748; Downloads: 38
URL Full text (0,00 KB)

6.
Classification of 2-arc-transitive dihedrants
Shao Fei Du, Aleksander Malnič, Dragan Marušič, 2008, original scientific article

Abstract: 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 ▫${\mathbb{F}}_q$▫.
Found in: ključnih besedah
Summary of found: ...dihedrants, that is, Cayley graphs of dihedral groups is given, thus completing the study of...
Keywords: permutation group, imprimitive group, dihedral group, Cayley graph, dihedrant, 2-Arc-transitive graph
Published: 15.10.2013; Views: 1555; Downloads: 46
URL Full text (0,00 KB)

7.
Primitive groups of degree twice a prime number
Dragan Marušič, 2012, unpublished invited conference lecture

Found in: ključnih besedah
Summary of found: ...primitive group, strongly regular graph, primitive action, ...
Keywords: primitive group, strongly regular graph, primitive action
Published: 15.10.2013; Views: 1581; Downloads: 23
URL Full text (0,00 KB)

8.
On quartic half-arc-transitive metacirculants
Dragan Marušič, Primož Šparl, 2008, original scientific article

Abstract: 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.
Found in: ključnih besedah
Summary of found: ...graph is a graph admitting a transitive group generated by two automorphisms ▫$\rho$▫ and ▫$\sigma$▫,...
Keywords: mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group
Published: 15.10.2013; Views: 1636; Downloads: 57
URL Full text (0,00 KB)

9.
The full automorphism group of a Cayley graph
Gabriel Verret, 2013, published scientific conference contribution abstract (invited lecture)

Found in: ključnih besedah
Keywords: automorphism group, Cayley graph
Published: 15.10.2013; Views: 2243; Downloads: 19
URL Full text (0,00 KB)
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10.
Distance-regular Cayley graphs on dihedral groups
Štefko Miklavič, Primož Potočnik, 2007, original scientific article

Abstract: 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.
Found in: ključnih besedah
Summary of found: ...classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such...
Keywords: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set
Published: 15.10.2013; Views: 1235; Downloads: 54
URL Full text (0,00 KB)

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