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51.
Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups
Štefko Miklavič, Primož Šparl, 2012, izvirni znanstveni članek

Opis: In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph ▫$\Gamma$▫ is ▫$n$▫-HC-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton cycle of ▫$\Gamma$▫. Similarly, ▫$\Gamma$▫ is weakly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton path of ▫$\Gamma$▫. Moreover, ▫$\Gamma$▫ is strongly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if for every such path $P$ there is a Hamilton path of ▫$\Gamma$▫ starting with ▫$P$▫. These concepts are then studied for the class of connected Cayley graphs on abelian groups. It is proved that every connected Cayley graph on an abelian group of order at least three is 2-HC-extendable and a complete classification of 3-HC-extendable connected Cayley graphs of abelian groups is obtained. Moreover, it is proved that every connected Cayley graph on an abelian group of order at least five is weakly 4-HP-extendable.
Najdeno v: ključnih besedah
Povzetek najdenega: ...path (HP) extendability are introduced. A connected graph ▫$\Gamma$▫ is ▫$n$▫-HC-extendable if it contains a...
Ključne besede: graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group
Objavljeno: 15.10.2013; Ogledov: 1208; Prenosov: 68
URL Polno besedilo (0,00 KB)

52.
Semiregular automorphisms of arc-transitive graphs
Gabriel Verret, 2013, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...automorphism group, arc-transitive graph, semiregular automorphism, ...
Ključne besede: automorphism group, arc-transitive graph, semiregular automorphism
Objavljeno: 15.10.2013; Ogledov: 1687; Prenosov: 20
URL Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

53.
Cubic Cayley graphs and snarks
Klavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2012, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley graph, snark, arc-transitive graph, Cayley map, ...
Ključne besede: Cayley graph, snark, arc-transitive graph, Cayley map
Objavljeno: 15.10.2013; Ogledov: 1184; Prenosov: 41
URL Polno besedilo (0,00 KB)

54.
On the order of arc-stabilizers in arc-transitive graphs
Gabriel Verret, 2009, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...arc-transitivie graph, arc-stabilizer, automorphism group, ...
Ključne besede: arc-transitivie graph, arc-stabilizer, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1492; Prenosov: 22
URL Polno besedilo (0,00 KB)

55.
Classification of cubic symmetric tetracirculants and pentacirculants
Boštjan Frelih, Klavdija Kutnar, 2013, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...cubic graph, symmetric, semiregular automorphism, tetracirculant, pentacirculant, ...
Ključne besede: cubic graph, symmetric, semiregular automorphism, tetracirculant, pentacirculant
Objavljeno: 15.10.2013; Ogledov: 1308; Prenosov: 44
URL Polno besedilo (0,00 KB)

56.
Special issue of discrete mathematics on Hamiltonicity problem for vertex-transitive (Cayley) graphs
Dragan Marušič, 2009, predgovor, spremna beseda

Najdeno v: ključnih besedah
Povzetek najdenega: ...Hamilton cycle, Hamilton path, Vetrex-transitive graph, Cayley graph, ...
Ključne besede: Hamilton cycle, Hamilton path, Vetrex-transitive graph, Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1277; Prenosov: 13
URL Polno besedilo (0,00 KB)

57.
Hamiltonian cycles in Cayley graphs whose order has few prime factors
Klavdija Kutnar, Dragan Marušič, D. W. Morris, Joy Morris, Primož Šparl, 2012, izvirni znanstveni članek

Opis: We prove that if Cay▫$(G; S)$▫ is a connected Cayley graph with ▫$n$▫ vertices, and the prime factorization of ▫$n$▫ is very small, then Cay▫$(G; S)$▫ has a hamiltonian cycle. More precisely, if ▫$p$▫, ▫$q$▫, and ▫$r$▫ are distinct primes, then ▫$n$▫ can be of the form kp with ▫$24 \ne k < 32$▫, or of the form ▫$kpq$▫ with ▫$k \le 5$▫, or of the form ▫$pqr$▫, or of the form ▫$kp^2$▫ with ▫$k \le 4$▫, or of the form ▫$kp^3$▫ with ▫$k \le 2$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...if Cay▫$(G; S)$▫ is a connected Cayley graph with ▫$n$▫ vertices, and the prime factorization...
Ključne besede: graph theory, Cayley graphs, hamiltonian cycles
Objavljeno: 15.10.2013; Ogledov: 1537; Prenosov: 57
URL Polno besedilo (0,00 KB)

58.
Distance-transitive graphs admit semiregular automorphisms
Klavdija Kutnar, Primož Šparl, 2010, izvirni znanstveni članek

Opis: A distance-transitive graph is a graph in which for every two ordered pairs ofvertices ▫$(u,v)$▫ and ▫$(u',v')$▫ such that the distance between ▫$u$▫ and ▫$v$▫ is equal to the distance between ▫$u'$▫ and ▫$v'$▫ there exists an automorphism of the graph mapping ▫$u$▫ to ▫$u'$▫ and ▫$v$▫ to ▫$v'$▫. A semiregular element of a permutation group is anon-identity element having all cycles of equal length in its cycle decomposition. It is shown that every distance-transitive graph admits a semiregular automorphism.
Najdeno v: ključnih besedah
Povzetek najdenega: ...A distance-transitive graph is a graph in which for every...
Ključne besede: distance-transitive graph, vertex-transitive graph, semiregular automorphism, permutation group
Objavljeno: 15.10.2013; Ogledov: 1618; Prenosov: 50
URL Polno besedilo (0,00 KB)

59.
Arc-transitive cycle decompositions of tetravalent graphs
Štefko Miklavič, Primož Potočnik, Stephen Wilson, 2008, izvirni znanstveni članek

Opis: A cycle decomposition of a graph ▫$\Gamma$▫ is a set ▫$\mathcal{C}$▫ of cycles of ▫$\Gamma$▫ such that every edge of ▫$\Gamma$▫ belongs to exactly one cycle in ▫$\mathcal{C}$▫. Such a decomposition is called arc-transitive if the group of automorphisms of ▫$\Gamma$▫ that preserve setwise acts transitively on the arcs of ▫$\Gamma$▫. In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining and enumerating arc-transitive cycle decompositions admitted by a given arc-transitive tetravalent graph. Among other results we show that a connected tetravalent arc-transitive graph is either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits exactly one cycle structure.
Najdeno v: ključnih besedah
Povzetek najdenega: ...A cycle decomposition of a graph ▫$\Gamma$▫ is a set ▫$\mathcal{C}$▫ of cycles...
Ključne besede: mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps
Objavljeno: 15.10.2013; Ogledov: 1345; Prenosov: 43
URL Polno besedilo (0,00 KB)

60.
Edge regular graph products
Boštjan Frelih, Štefko Miklavič, 2013, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: Zadetek v naslovu
Ključne besede: edge regular graph, strong product, lexicographic product, deleted lexicographic product, co-normal product
Objavljeno: 15.10.2013; Ogledov: 1234; Prenosov: 19
URL Polno besedilo (0,00 KB)

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