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1.
Quasi m-Cayley circulants
Ademir Hujdurović, 2013, published scientific conference contribution

Abstract: A graph ▫$\Gamma$▫ is called a quasi ▫$m$▫-Cayley graph on a group ▫$G$▫ if there exists a vertex ▫$\infty \in V(\Gamma)$▫ and a subgroup ▫$G$▫ of the vertex stabilizer ▫$\text{Aut}(\Gamma)_\infty$▫ of the vertex ▫$\infty$▫ in the full automorphism group ▫$\text{Aut}(\Gamma)$▫ of ▫$\Gamma$▫, such that ▫$G$▫ acts semiregularly on ▫$V(\Gamma) \setminus \{\infty\}$▫ with ▫$m$▫ orbits. If the vertex ▫$\infty$▫ is adjacent to only one orbit of ▫$G$▫ on ▫$V(\Gamma) \setminus \{\infty\}$▫, then ▫$\Gamma$▫ is called a strongly quasi ▫$m$▫-Cayley graph on ▫$G$▫ .In this paper complete classifications of quasi 2-Cayley, quasi 3-Cayley and strongly quasi 4-Cayley connected circulants are given.
Found in: ključnih besedah
Summary of found: ...arc-transitive, circulant, quasi m-Cayley graph...
Keywords: arc-transitive, circulant, quasi m-Cayley graph
Published: 15.10.2013; Views: 1712; Downloads: 59
URL Full text (0,00 KB)

2.
On Hamiltonicity of circulant digraphs of outdegree three
Štefko Miklavič, Primož Šparl, 2009, original scientific article

Abstract: This paper deals with Hamiltonicity of connected loopless circulant digraphs of outdegree three with connection set of the form ▫$\{a,ka,c\}$▫, where ▫$k$▫ is an integer. In particular, we prove that if ▫$k=-1$▫ or ▫$k=2$▫ such a circulant digraph is Hamiltonian if and only if it is not isomorphic to the circulant digraph on 12 vertices with connection set ▫$\{3,6,4\}$▫.
Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: graph theory, circulant digraph, Hamilton cycle
Published: 15.10.2013; Views: 1322; Downloads: 51
URL Full text (0,00 KB)

3.
Algebraični aspekti teorije grafov
Ademir Hujdurović, 2013, doctoral dissertation

Found in: ključnih besedah
Summary of found: ...circulant, bicirculant, semiregular automorphism, vertex-transitive graph, half-arc-transi...
Keywords: circulant, bicirculant, semiregular automorphism, vertex-transitive graph, half-arc-transitive graph, snark, Cayley graph, quasi m-Cayley graph, generalized Cayley graph, I-regular action, regular cover of a graph, automorphism group
Published: 10.07.2015; Views: 1575; Downloads: 4
URL Full text (0,00 KB)

4.
Symmetry structure of bicirculants
Boštjan 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: ključnih besedah
Summary of found: ...mathematics, graph theory, graph, circulant, bicirculant, automorphism group...
Keywords: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Published: 03.04.2017; Views: 1003; Downloads: 55
URL Full text (0,00 KB)

5.
On strongly regular bicirculants
Dragan 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 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.
Found in: ključnih besedah
Summary of found: ...mathematics, graph theory, graph, circulant, bicirculant, automorphism group...
Keywords: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Published: 03.04.2017; Views: 1101; Downloads: 49
URL Full text (0,00 KB)

6.
Automorphism groups of circulant digraphs with applications to semigroup theory
Joao Araújo, Wolfram Bentz, Edward Dobson, Janusz Konieczny, Joy Morris, 2018, original scientific article

Found in: ključnih besedah
Summary of found: Zadetek v naslovu
Keywords: automorphism group, circulant digraph, semigroup
Published: 08.05.2018; Views: 869; Downloads: 79
URL Full text (0,00 KB)

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