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11.
Rose window graphs underlying rotary maps
István Kovács, Klavdija Kutnar, János Ruff, 2010, published scientific conference contribution

Abstract: 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 ▫$\{\{x_i, x_{i+1}\} \vert\; i \in {\mathbb Z}_n \} \cup \{\{y_i, y_{i+1}\} \vert\; i \in {\mathbb Z}_n \} \cup \{\{x_i, y_i\} \vert\; i \in {\mathbb Z}_n\} \cup \{\{x_{i+a}, y_i\} \vert\; i \in {\mathbb Z}_n \}$▫. In this paper rotary maps on rose window graphs are considered. In particular, we answer the question posed in [S. Wilson, Rose window graphs, Ars Math. Contemp. 1 (2008), 7-19. http://amc.imfm.si/index.php/amc/issue/view/5] concerning which of these graphs underlie a rotary map.
Found in: osebi
Keywords: graph theory, rotary map, edge-transitive graph, covering graph, voltage graph
Published: 15.10.2013; Views: 1583; Downloads: 48
URL Full text (0,00 KB)

12.
Hamilton paths and cycles in vertex-transitive graphs
Klavdija Kutnar, 2008, invited lecture at foreign university

Found in: osebi
Published: 15.10.2013; Views: 2075; Downloads: 11
URL Full text (0,00 KB)

13.
The strongly distance-balanced property of the generalized Petersen graphs
Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, Štefko Miklavič, 2009, original scientific article

Abstract: A graph ▫$X$▫ is said to be strongly distance-balanced whenever for any edge ▫$uv$▫ of ▫$X$▫ and any positive integer ▫$i$▫, the number of vertices at distance ▫$i$▫ from ▫$u$▫ and at distance ▫$i + 1$▫ from ▫$v$▫ is equal to the number of vertices at distance ▫$i + 1$▫ from ▫$u$▫ and at distance ▫$i$▫ from ▫$v$▫. It is proven that for any integers ▫$k \ge 2$▫ and ▫$n \ge k^2 + 4k + 1$▫, the generalized Petersen graph GP▫$(n, k)$▫ is not strongly distance-balanced.
Found in: osebi
Keywords: graph, strongy distance-balanced, generalized Petersen graph
Published: 15.10.2013; Views: 1488; Downloads: 64
URL Full text (0,00 KB)

14.
Classification of symmetric Tabčjn graphs
Klavdija Kutnar, Aubin Arroyo, Adolfo Guillot, Isabel Hubard, 2012, unpublished invited conference lecture

Found in: osebi
Published: 15.10.2013; Views: 1046; Downloads: 14
URL Full text (0,00 KB)

15.
Hamilton cycles and paths in vertex-transitive graphs
Klavdija Kutnar, 2011, invited lecture at foreign university

Found in: osebi
Keywords: Hamilton cycles
Published: 15.10.2013; Views: 1223; Downloads: 12
URL Full text (0,00 KB)

16.
Hamiltonian cycles in Cayley graphs of order 12p
Klavdija Kutnar, 2005, invited lecture at foreign university

Found in: osebi
Published: 15.10.2013; Views: 1799; Downloads: 10
URL Full text (0,00 KB)

17.
Strongly regular tri-Cayley graphs
Klavdija Kutnar, Dragan Marušič, Štefko Miklavič, Primož Šparl, 2009, original scientific article

Abstract: 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.
Found in: osebi
Keywords: strongly regular graph, tri-Cayley graph
Published: 15.10.2013; Views: 1268; Downloads: 51
URL Full text (0,00 KB)

18.
Hamilton cycles and paths in vertex-transitive graphs
Klavdija Kutnar, 2010, invited lecture at foreign university

Found in: osebi
Keywords: Hamilton cycles
Published: 15.10.2013; Views: 1247; Downloads: 10
URL Full text (0,00 KB)

19.
Math 568 - Linear Algebra
Klavdija Kutnar, 2008, invited lecture at foreign university

Found in: osebi
Published: 15.10.2013; Views: 2675; Downloads: 13
URL Full text (0,00 KB)

20.
Hamiltonicity of cubic Cayley graphs
Dragan Marušič, Henry Glover, Klavdija Kutnar, Aleksander Malnič, 2012, published scientific conference contribution abstract (invited lecture)

Found in: osebi
Keywords: Cayley graph, Hamilton path, Hamilton cycle, arc-transitive graph, Cayley map
Published: 15.10.2013; Views: 1402; Downloads: 29
URL Full text (0,00 KB)

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