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51.
Editorial
Klavdija Kutnar, Štefko Miklavič, Tomaž Pisanski, Primož Šparl, 2015, predgovor, uvodnik, spremna beseda

Objavljeno v RUP: 15.10.2015; Ogledov: 2067; Prenosov: 24
URL Povezava na celotno besedilo

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A note on a geometric construction of large Cayley graps of given degree and diameter
György Kiss, István Kovács, Klavdija Kutnar, János Ruff, Primož Šparl, 2009, izvirni znanstveni članek

Opis: An infinite series and some sporadic examples of large Cayley graphs with given degree and diameter are constructed. The graphs arise from arcs, caps and other objects of finite projective spaces.
Ključne besede: degree, diameter problem, Moore bound, finite projective spaces
Objavljeno v RUP: 15.10.2013; Ogledov: 3341; Prenosov: 69
URL Povezava na celotno besedilo

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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.
Ključne besede: distance-transitive graph, vertex-transitive graph, semiregular automorphism, permutation group
Objavljeno v RUP: 15.10.2013; Ogledov: 3370; Prenosov: 98
URL Povezava na celotno besedilo

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 ▫$k \le 2$▫.
Ključne besede: graph theory, Cayley graphs, hamiltonian cycles
Objavljeno v RUP: 15.10.2013; Ogledov: 3500; Prenosov: 120
.pdf Celotno besedilo (545,91 KB)

58.
Bled'11
Klavdija Kutnar, Primož Šparl, 2013, predgovor, uvodnik, spremna beseda

Objavljeno v RUP: 15.10.2013; Ogledov: 2405; Prenosov: 65
URL Povezava na celotno besedilo

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

Ključne besede: Cayley graph, snark, arc-transitive graph, Cayley map
Objavljeno v RUP: 15.10.2013; Ogledov: 2991; Prenosov: 82
URL Povezava na celotno besedilo

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