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1.
On bipartite Q-polynomial distance-regular graphs with c [sub] 2 [equal] 1
Štefko Miklavič, 2007, izvirni znanstveni članek

Opis: Let ▫$\Gamma$▫ denote a bipartite ▫$Q$▫-polynomial distance-regular graph with diameter ▫$d \ge 3$▫, valency ▫$k \ge 3$▫ and intersection number ▫$c_2=1$▫. We show that ▫$\Gamma$▫ has a certain equitable partition of its vertex set which involves ▫$4d-4$▫ cells. We use this partition to show that the intersection numbers of ▫$\Gamma$▫ satisfy the following divisibility conditions: (I) ▫$c_{i+1}-1$▫ divides ▫$c_i(c_i-1)$▫ for ▫$2 \le i \le d-1$▫, and (II) ▫$b_{i-1}-1$▫ divides ▫$b_i(b_i-1)$▫ for ▫$1 \le i \le d-1$▫. Using these divisibility conditions we show that ▫$\Gamma$▫ does not exist if ▫$d=4$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...mathematics, grah theory, distance-regular graphs, ▫$Q$▫-polynomial property, equitable partitions...
Ključne besede: mathematics, grah theory, distance-regular graphs, ▫$Q$▫-polynomial property, equitable partitions
Objavljeno: 15.10.2013; Ogledov: 1605; Prenosov: 14
URL Polno besedilo (0,00 KB)

2.
Hamiltonicity of vertex-transitive graphs of order 4p
Klavdija Kutnar, Dragan Marušič, 2008, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group...
Ključne besede: graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1524; Prenosov: 17
URL Polno besedilo (0,00 KB)

3.
Coding theory and applications, cyclic codes
Enes Pašalić, 2013, drugo učno gradivo

Najdeno v: ključnih besedah
Povzetek najdenega: Zadetek v naslovu
Ključne besede: coding theory, cyclic codes, BCH codes, Reed-Solomon codes, channel erasures
Objavljeno: 15.10.2013; Ogledov: 1312; Prenosov: 27
URL Polno besedilo (0,00 KB)
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4.
Isomorphism checking of I-graphs
Boris Horvat, Tomaž Pisanski, Arjana Žitnik, 2012, izvirni znanstveni članek

Opis: We consider the class of ▫$I$▫-graphs, which is a generalization of the class of the generalized Petersen graphs. We show that two ▫$I$▫-graphs ▫$I(n, j, k)$▫ and ▫$I(n, j_1, k_1)$▫ are isomorphic if and only if there exists an integer ▫$a$▫ relatively prime to $n$ such that either ▫$\{j_1, k_1\} = \{aj \mod n, \; ak \mod n \}$▫ or ▫$\{j_1, k_1\} = \{aj \mod n, \; -ak \mod n\}$▫. This result has an application in the enumeration of non-isomorphic ▫$I$▫-graphs and unit-distance representations of generalized Petersen graphs.
Najdeno v: ključnih besedah
Povzetek najdenega: ...mathematics, graph theory, isomorphism, I-graph, generalized Petersen graph...
Ključne besede: mathematics, graph theory, isomorphism, I-graph, generalized Petersen graph
Objavljeno: 15.10.2013; Ogledov: 1437; Prenosov: 58
URL Polno besedilo (0,00 KB)

5.
Distance-balanced graphs: Symmetry conditions
Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, Štefko Miklavič, 2006, izvirni znanstveni članek

Opis: A graph ▫$X$▫ is said to be distance-balanced if for any edge ▫$uv$▫ of ▫$X$▫, the number of vertices closer to ▫$u$▫ than to ▫$v$▫ is equal to the number of vertices closer to ▫$v$▫ than to ▫$u$▫. A graph ▫$X$▫ is said to be strongly distance-balanced if for any edge ▫$uv$▫ of ▫$X$▫ and any integer ▫$k$▫, the number of vertices at distance ▫$k$▫ from ▫$u$▫ and at distance ▫$k+1$▫ from ▫$v$▫ is equal to the number of vertices at distance ▫$k+1$▫ from ▫$u$▫ and at distance ▫$k$▫ from ▫$v$▫. Exploring the connection between symmetry properties of graphs and the metric property of being (strongly) distance-balanced is the main theme of this article. That a vertex-transitive graph is necessarily strongly distance-balanced and thus also distance-balanced is an easy observation. With only a slight relaxation of the transitivity condition, the situation changes drastically: there are infinite families of semisymmetric graphs (that is, graphs which are edge-transitive, but not vertex-transitive) which are distance-balanced, but there are also infinite families of semisymmetric graphs which are not distance-balanced. Results on the distance-balanced property in product graphs prove helpful in obtaining these constructions. Finally, a complete classification of strongly distance-balanced graphs is given for the following infinite families of generalized Petersen graphs: GP▫$(n,2)$▫, GP▫$(5k+1,k)$▫, GP▫$(3k 3,k)$▫, and GP▫$(2k+2,k)$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...graph theory, graph, distance-balanced graphs, vertex-transitive, semysimmetric, generalized ...
Ključne besede: graph theory, graph, distance-balanced graphs, vertex-transitive, semysimmetric, generalized Petersen graph
Objavljeno: 15.10.2013; Ogledov: 1744; Prenosov: 37
URL Polno besedilo (0,00 KB)

6.
A complete classification of cubic symmetric graphs of girth 6
Klavdija Kutnar, Dragan Marušič, 2009, izvirni znanstveni članek

Opis: A complete classification of cubic symmetric graphs of girth 6 is given. It is shown that with the exception of the Heawood graph, the Moebius-Kantor graph, the Pappus graph, and the Desargues graph, a cubic symmetric graph ▫$X$▫ of girth 6 is a normal Cayley graph of a generalized dihedral group; in particular, (i) ▫$X$▫ is 2-regular if and only if it is isomorphic to a so-called ▫$I_k^n$▫-path, a graph of order either ▫$n^2/2$▫ or ▫$n^2/6$▫, which is characterized by the fact that its quotient relative to a certain semiregular automorphism is a path. (ii) ▫$X$▫ is 1-regular if and only if there exists an integer ▫$r$▫ with prime decomposition ▫$r=3^s p_1^{e_1} \dots p_t^{e_t} > 3$▫, where ▫$s \in \{0,1\}$▫, ▫$t \ge 1$▫, and ▫$p_i \equiv 1 \pmod{3}$▫, such that ▫$X$▫ is isomorphic either to a Cayley graph of a dihedral group ▫$D_{2r}$▫ of order ▫$2r$▫ or ▫$X$▫ is isomorphic to a certain ▫$\ZZ_r$▫-cover of one of the following graphs: the cube ▫$Q_3$▫, the Pappus graph or an ▫$I_k^n(t)$▫-path of order ▫$n^2/2$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...graph theory, cubic graphs, symmetric graphs, ▫$s$▫-regular graphs, girth,...
Ključne besede: graph theory, cubic graphs, symmetric graphs, ▫$s$▫-regular graphs, girth, consistent cycle
Objavljeno: 15.10.2013; Ogledov: 1740; Prenosov: 36
URL Polno besedilo (0,00 KB)

7.
Rose window graphs underlying rotary maps
István Kovács, Klavdija Kutnar, János Ruff, 2010, objavljeni znanstveni prispevek na konferenci

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...graph theory, rotary map, edge-transitive graph, covering graph, voltage...
Ključne besede: graph theory, rotary map, edge-transitive graph, covering graph, voltage graph
Objavljeno: 15.10.2013; Ogledov: 1482; Prenosov: 35
URL Polno besedilo (0,00 KB)

8.
Q-polynomial distance-regular graphs with a [sub] 1 [equal] 0 and a [sub] 2 [not equal] 0
Štefko Miklavič, 2008, izvirni znanstveni članek

Opis: Let ▫$\Gamma$▫ denote a ▫$Q$▫-polynomial distance-regular graph with diameter ▫$D \ge 3$▫ and intersection numbers ▫$a_1=0$▫, ▫$a_2 \ne 0$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫$\Gamma$▫. Fix ▫$x \in X$▫ and let denote $A^\ast \in {\mathrm{Mat}}_X ({\mathbb{C}})$ the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫$A{\mathrm{Mat}}_X ({\mathbb{C}})$▫ generated by ▫$A$▫, ▫$A^\ast$▫. We call ▫$T$▫ the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. We show that up to isomorphism there exists a unique irreducible ▫$T$▫-module ▫$W$▫ with endpoint 1. We show that ▫$W$▫ has dimension ▫$2D-2$▫. We display a basis for ▫$W$▫ which consists of eigenvectors for ▫$A^\ast$▫. We display the action of ▫$A$▫ on this basis. We show that ▫$W$▫ appears in the standard module of ▫$\Gamma$▫ with multiplicity ▫$k-1$▫, where ▫$k$▫ is the valency of ▫$\Gamma$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...mathematics, graph theory, adjacency matrix, distance-regular graph, Terwilliger algebra...
Ključne besede: mathematics, graph theory, adjacency matrix, distance-regular graph, Terwilliger algebra
Objavljeno: 15.10.2013; Ogledov: 1391; Prenosov: 9
URL Polno besedilo (0,00 KB)

9.
On quartic half-arc-transitive metacirculants
Dragan Marušič, Primož Šparl, 2008, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism...
Ključne besede: mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1580; Prenosov: 48
URL Polno besedilo (0,00 KB)

10.
Consistent Cycles in 1/2-Arc-Transitive Graphs
Marko Boben, Štefko Miklavič, Primož Potočnik, 2009, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...mathematics, graph theory, 1/2-arc-transitivity, consistent cycle, ...
Ključne besede: mathematics, graph theory, 1/2-arc-transitivity, consistent cycle
Objavljeno: 15.10.2013; Ogledov: 2083; Prenosov: 7
URL Polno besedilo (0,00 KB)
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