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1.
On prime-valent symmetric bicirculants and Cayley snarks
Ademir Hujdurović, Klavdija Kutnar, Dragan Marušič, 2013, objavljeni znanstveni prispevek na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ... graph, Cayley graph, arc-transitive, snark, semiregular automorphism, bicirculant,...
Ključne besede: graph, Cayley graph, arc-transitive, snark, semiregular automorphism, bicirculant
Objavljeno: 15.10.2013; Ogledov: 1496; Prenosov: 58
URL Polno besedilo (0,00 KB)

2.
The full automorphism group of Cayley graphs of ${mathbb Z}_ptimes{mathbbZ}_{p^2}$
Edward Dobson, 2012, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley graph, abelian group, automorphism group, ...
Ključne besede: Cayley graph, abelian group, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1689; Prenosov: 30
URL Polno besedilo (0,00 KB)

3.
On non-normal arc-transitive 4-valent dihedrants
István Kovács, Boštjan Kuzman, Aleksander Malnič, 2010, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...▫$X$▫ be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral group ▫$D_n$▫ such...
Ključne besede: Cayley graph, arc transitivity, dihedral group
Objavljeno: 15.10.2013; Ogledov: 1681; Prenosov: 31
URL Polno besedilo (0,00 KB)

4.
Classification of 2-arc-transitive dihedrants
Shao Fei Du, Aleksander Malnič, Dragan Marušič, 2008, izvirni znanstveni članek

Opis: 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 besedah
Povzetek najdenega: ...complete classification of 2-arc-transitive dihedrants, that is, Cayley graphs of dihedral groups is given, thus...
Ključne besede: permutation group, imprimitive group, dihedral group, Cayley graph, dihedrant, 2-Arc-transitive graph
Objavljeno: 15.10.2013; Ogledov: 1477; Prenosov: 30
URL Polno besedilo (0,00 KB)

5.
The full automorphism group of a Cayley graph
Gabriel Verret, 2013, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Najdeno v: ključnih besedah
Ključne besede: automorphism group, Cayley graph
Objavljeno: 15.10.2013; Ogledov: 2165; Prenosov: 17
URL Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

6.
Strongly regular tri-Cayley graphs
Klavdija Kutnar, Dragan Marušič, Štefko Miklavič, Primož Šparl, 2009, izvirni znanstveni članek

Opis: A graph is called tri-Cayley if it admits a semiregular subgroup of automorphisms having three orbits of equal length. In this paper, the structure of strongly regular tri-Cayley graphs is investigated. A structural description of strongly regular tri-Cayley graphs of cyclic groups is given.
Najdeno v: ključnih besedah
Povzetek najdenega: ...A graph is called tri-Cayley if it admits a...
Ključne besede: strongly regular graph, tri-Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1178; Prenosov: 29
URL Polno besedilo (0,00 KB)

7.
Distance-regular Cayley graphs on dihedral groups
Štefko Miklavič, Primož Potočnik, 2007, izvirni znanstveni članek

Opis: 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 besedah
Povzetek najdenega: ...article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious...
Ključne besede: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set
Objavljeno: 15.10.2013; Ogledov: 1165; Prenosov: 37
URL Polno besedilo (0,00 KB)

8.
Hamiltonicity of cubic Cayley graphs
Dragan Marušič, Henry Glover, Klavdija Kutnar, Aleksander Malnič, 2012, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley graph, Hamilton path, Hamilton cycle, arc-transitive graph, Cayley...
Ključne besede: Cayley graph, Hamilton path, Hamilton cycle, arc-transitive graph, Cayley map
Objavljeno: 15.10.2013; Ogledov: 1304; Prenosov: 20
URL Polno besedilo (0,00 KB)

9.
Construction of Hamilton cycles in (2,s,3)-Cayley graphs
Klavdija Kutnar, 2010, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...Hamilton cycle, Cayley graph, ...
Ključne besede: Hamilton cycle, Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1252; Prenosov: 8
URL Polno besedilo (0,00 KB)

10.
Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order
Edward Dobson, 2010, izvirni znanstveni članek

Opis: We show that almost every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of ▫$G$▫ (that is, ▫$G_L \triangleleft {\rm Aut}(\Gamma))$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...We show that almost every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of...
Ključne besede: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-group
Objavljeno: 15.10.2013; Ogledov: 2333; Prenosov: 35
URL Polno besedilo (0,00 KB)

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