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13. A note on a geometric construction of large Cayley graps of given degree and diameterGyörgy Kiss, István Kovács, Klavdija Kutnar, János Ruff, Primož Šparl, 2009, original scientific article Abstract: 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. Found in: osebi Keywords: degree, diameter problem, Moore bound, finite projective spaces Published: 15.10.2013; Views: 1697; Downloads: 24 Full text (0,00 KB) This document has more files! More...

14. Simetrije cirkulantnih grafovMaruša Saksida, 2014, master's thesis Found in: osebi Keywords: cirkulantni graf, točkovna tranzitivnost, povezavna tranzitivnost, ločna tranzitivnost, izomorfizem, grupa avtomorfizmov, ciklični indeks, normalen cirkulant Published: 10.07.2015; Views: 2194; Downloads: 16 Full text (0,00 KB) This document has more files! More...

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16. Reachability relations in digraphsNorbert Seifter, Boris Zgrablić, Aleksander Malnič, Primož Šparl, Dragan Marušič, 2008, original scientific article Abstract: 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 0weighted 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 0weighted 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. Found in: osebi Keywords: graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth Published: 03.04.2017; Views: 944; Downloads: 91 Full text (0,00 KB) 
17. Symmetry structure of bicirculantsBoštjan Frelih, Primož Šparl, Aleksander Malnič, Dragan Marušič, 2007, original scientific article Abstract: 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. Found in: osebi Keywords: mathematics, graph theory, graph, circulant, bicirculant, automorphism group Published: 03.04.2017; Views: 1047; Downloads: 59 Full text (0,00 KB) 
18. On strongly regular bicirculantsDragan Marušič, Aleksander Malnič, Primož Šparl, 2007, original scientific article Abstract: 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 8bicirculants, no other example seems to be known. A necessary condition for the existence of a strongly regular vertextransitive ▫$p$▫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 vertextransitive but not edgetransitive. Found in: osebi Keywords: mathematics, graph theory, graph, circulant, bicirculant, automorphism group Published: 03.04.2017; Views: 1168; Downloads: 54 Full text (0,00 KB) 
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