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11.
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14.
l-distance-balanced graphs
Štefko Miklavič, Primož Šparl, 2018, izvirni znanstveni članek

Ključne besede: distance-balanced, l-distance-balanced, highly distance-balanced
Objavljeno v RUP: 05.04.2018; Ogledov: 2224; Prenosov: 98
URL Povezava na celotno besedilo

15.
On structural results of tetravalent half-arc-transitive graphs
Primož Šparl, 2018, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: graph, half-arc-transitive, alternating cycle, radius
Objavljeno v RUP: 07.02.2018; Ogledov: 2047; Prenosov: 27
URL Povezava na celotno besedilo

16.
Reachability relations in digraphs
Aleksander Malnič, Dragan Marušič, Norbert Seifter, Primož Šparl, Boris Zgrablić, 2008, izvirni znanstveni članek

Opis: In this paper we study reachability relations on vertices of digraphs, informally defined as follows. First, the weight of a walk is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed in the direction opposite to their orientation. Then, a vertex ▫$u$▫ is ▫$R_k^+$▫-related to a vertex ▫$v$▫ if there exists a 0-weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at u has weight in the interval ▫$[0,k]$▫. Similarly, a vertex ▫$u$▫ is ▫$R_k^-$▫-related to a vertex ▫$v$▫ if there exists a 0-weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at ▫$u$▫ has weight in the interval ▫$[-k,0]$▫. For all positive integers ▫$k$▫, the relations ▫$R_k^+$▫ and ▫$R_k^-$▫ are equivalence relations on the vertex set of a given digraph. We prove that, for transitive digraphs, properties of these relations are closely related to other properties such as having property ▫$\mathbb{Z}$▫, the number of ends, growth conditions, and vertex degree.
Ključne besede: graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth
Objavljeno v RUP: 03.04.2017; Ogledov: 2680; Prenosov: 133
URL Povezava na celotno besedilo

17.
Symmetry structure of bicirculants
Aleksander Malnič, Dragan Marušič, Primož Šparl, Boštjan Frelih, 2007, izvirni znanstveni članek

Opis: An ▫$n$▫-bicirculant is a graph having an automorphism with two orbits of length ▫$n$▫ and no other orbits. Symmetry properties of ▫$p$▫-bicirculants, ▫$p$▫ a prime, are extensively studied. In particular, the actions of their automorphism groups are described in detail in terms of certain algebraic representation of such graphs.
Ključne besede: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Objavljeno v RUP: 03.04.2017; Ogledov: 2446; Prenosov: 95
URL Povezava na celotno besedilo

18.
On strongly regular bicirculants
Aleksander Malnič, Dragan Marušič, Primož Šparl, 2007, izvirni znanstveni članek

Opis: An ▫$n$▫-bicirculantis a graph having an automorphism with two orbits of length ▫$n$▫ and no other orbits. This article deals with strongly regular bicirculants. It is known that for a nontrivial strongly regular ▫$n$▫-bicirculant, ▫$n$▫ odd, there exists a positive integer m such that ▫$n=2m^2+2m+1▫$. Only three nontrivial examples have been known previously, namely, for ▫$m=1,2$▫ and 4. Case ▫$m=1$▫ gives rise to the Petersen graph and its complement, while the graphs arising from cases ▫$m=2$▫ and ▫$m=4$▫ are associated with certain Steiner systems. Similarly, if ▫$n$▫ is even, then ▫$n=2m^2$▫ for some ▫$m \ge 2$▫. Apart from a pair of complementary strongly regular 8-bicirculants, no other example seems to be known. A necessary condition for the existence of a strongly regular vertex-transitive ▫$p$▫-bicirculant, ▫$p$▫ a prime, is obtained here. In addition, three new strongly regular bicirculants having 50, 82 and 122 vertices corresponding, respectively, to ▫$m=3,4$▫ and 5 above, are presented. These graphs are not associated with any Steiner system, and together with their complements form the first known pairs of complementary strongly regular bicirculants which are vertex-transitive but not edge-transitive.
Ključne besede: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Objavljeno v RUP: 03.04.2017; Ogledov: 3316; Prenosov: 88
URL Povezava na celotno besedilo

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20.
Editorial
Klavdija Kutnar, Štefko Miklavič, Tomaž Pisanski, Primož Šparl, 2015, predgovor, uvodnik, spremna beseda

Objavljeno v RUP: 15.10.2015; Ogledov: 1995; Prenosov: 24
URL Povezava na celotno besedilo

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