1. On the wreath product of signed and gain graphs and its spectrumMatteo Cavaleri, Alfredo Donno, Stefano Spessato, 2025, izvirni znanstveni članek Opis: We introduce a notion of wreath product of two gain graphs (Γ_1, ψ_1, G_1) and (Γ_2, ψ_2, G_2), producing a gain graph over the direct product group G_2|V_Γ1| × G_1, whose underlying graph is the classical wreath product of graphs Γ_1≀Γ_2. By composition with a suitable group homomorphism, our construction produces a signed graph when the two factors are signed graphs. We prove that the wreath product is stable under switching isomorphism. By using group representations, we are able to perform spectral computations on the wreath product: in particular, we determine its largest and its smallest eigenvalue, and we give a description of the spectrum when the first factor is a complex unit complete balanced or antibalanced gain graph, and the second factor is circulant. Finally, when G_1 is a group of permutations of the vertex set of the first factor, and the group G_2 is abelian, we give an alternative definition producing a gain graph over the group wreath product G_1≀G_2, which turns out to be stable under switching equivalence of the second factor, when the first factor is balanced.
Ključne besede: gain graph, signed graph, wreath product of graphs, wreath product of groups, circulant gain graph, mixed Kronecker product, π-spectrum
Objavljeno v RUP: 22.10.2025; Ogledov: 379; Prenosov: 5
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2. Posplošitev Lijeve domneve in popolna klasifikacija cikličnih m-(D)CI-grup : magistrsko deloLuka Šinkovec, 2023, magistrsko delo Ključne besede: (un)directed Cayley graph, cyclic group, (un)directed circulant graph, Cayley isomorphism, (un)directed CI-graph, (D)CI-group, m-(D)CI-group, key, generalised multiplier
Objavljeno v RUP: 11.09.2023; Ogledov: 2053; Prenosov: 30
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5. Symmetry structure of bicirculantsAleksander 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: 4049; Prenosov: 104
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6. On strongly regular bicirculantsAleksander 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: 11009; Prenosov: 99
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7. Algebraični aspekti teorije grafov : doktorska disertacijaAdemir Hujdurović, 2013, doktorska disertacija Ključne besede: 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
Objavljeno v RUP: 10.07.2015; Ogledov: 6012; Prenosov: 53
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8. On Hamiltonicity of circulant digraphs of outdegree threeŠtefko Miklavič, Primož Šparl, 2009, izvirni znanstveni članek Opis: 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 ▫$\{3,6,4\}$▫.
Ključne besede: graph theory, circulant digraph, Hamilton cycle
Objavljeno v RUP: 15.10.2013; Ogledov: 5026; Prenosov: 109
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9. Quasi m-Cayley circulantsAdemir Hujdurović, 2013, objavljeni znanstveni prispevek na konferenci Opis: 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.
Ključne besede: arc-transitive, circulant, quasi m-Cayley graph
Objavljeno v RUP: 15.10.2013; Ogledov: 4878; Prenosov: 122
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