# Search the repository

 Query: search in TitleAuthorAbstractKeywordsFull textYear of publishing ANDORAND NOT search in TitleAuthorAbstractKeywordsFull textYear of publishing ANDORAND NOT search in TitleAuthorAbstractKeywordsFull textYear of publishing ANDORAND NOT search in TitleAuthorAbstractKeywordsFull textYear of publishing Work type: All work types Habilitation (m4) Specialist thesis (m3) High school thesis (m6) Bachelor work * (dip) Master disertations * (mag) Doctorate disertations * (dok) Research Data or Corpuses (data) * old and bolonia study programme Language: All languagesSlovenianEnglishGermanCroatianSerbianBosnianBulgarianCzechFinnishFrenchGerman (Austria)HungarianItalianJapaneseLithuanianNorwegianPolishRussianSerbian (cyrillic)SlovakSpanishSwedishTurkishUnknown Search in: RUP    FAMNIT - Faculty of Mathematics, Science and Information Technologies    FHŠ - Faculty of Humanities    FM - Faculty of Management    FTŠ Turistica - Turistica – College of Tourism Portorož    FVZ - Faculty of Health Sciences    IAM - Andrej Marušič Institute    PEF - Faculty of Education    UPR - University of PrimorskaCOBISS    Fakulteta za humanistične študije, Koper    Fakulteta za management Koper in Pedagoška fakulteta Koper    Fakulteta za vede o zdravju, Izola    Knjižnica za tehniko, medicino in naravoslovje, Koper    Turistica, Portorož    Znanstveno-raziskovalno središče Koper Options: Show only hits with full text Reset

 31 - 40 / 7112345678 31.Hamilton cycles in (2, odd, 3)-Cayley graphsHenry Glover, Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, 2012, original scientific articleAbstract: In 1969, Lovász asked if every finite, connected vertex-transitive graph has a Hamilton path. In spite of its easy formulation, no major breakthrough has been achieved thus far, and the problem is now commonly accepted to be very hard. The same holds for the special subclass of Cayley graphs where the existence of Hamilton cycles has been conjectured. In 2007, Glover and Marušič proved that a cubic Cayley graph on a finite ▫$(2, s, 3)$▫-generated group ▫$G = \langle a, x| a^2 = x^s = (ax)^3 = 1, \dots \rangle$▫ has a Hamilton path when ▫$|G|$▫ is congruent to 0 modulo 4, and has a Hamilton cycle when ▫$|G|$▫ is congruent to 2 modulo 4. The Hamilton cycle was constructed, combining the theory of Cayley maps with classical results on cyclic stability in cubic graphs, as the contractible boundary of a tree of faces in the corresponding Cayley map. With a generalization of these methods, Glover, Kutnar and Marušič in 2009 resolved the case when, apart from ▫$|G|$▫, also ▫$s$▫ is congruent to 0 modulo 4. In this article, with a further extension of the above "tree of faces" approach, a Hamilton cycle is shown to exist whenever ▫$|G|$▫ is congruent to 0 modulo 4 and s is odd. This leaves ▫$|G|$▫ congruent to 0 modulo 4 with s congruent to 2 modulo 4 as the only remaining open case. In this last case, however, the "tree of faces" approach cannot be applied, and so entirely different techniques will have to be introduced if one is to complete the proof of the existence of Hamilton cycles in cubic Cayley graphs arising from finite ▫$(2, s, 3)$▫-generated groups.Found in: osebiSummary of found: ...has been conjectured. In 2007, Glover and Marušič proved that a cubic Cayley graph on...Keywords: Cayley graph, Hamilton cycle, arc-transitive graph, 1-regular action, automorphism groupPublished: 15.10.2013; Views: 1288; Downloads: 66 Full text (0,00 KB) 32.Cubic Cayley graphs and snarksKlavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2012, published scientific conference contribution abstract (invited lecture)Found in: osebiKeywords: Cayley graph, snark, arc-transitive graph, Cayley mapPublished: 15.10.2013; Views: 1323; Downloads: 50 Full text (0,00 KB) 33.Special issue of discrete mathematics on Hamiltonicity problem for vertex-transitive (Cayley) graphsDragan Marušič, 2009, preface, afterwordFound in: osebiKeywords: Hamilton cycle, Hamilton path, Vetrex-transitive graph, Cayley graphPublished: 15.10.2013; Views: 1410; Downloads: 14 Full text (0,00 KB) 34.Hamiltonian cycles in Cayley graphs whose order has few prime factorsKlavdija Kutnar, Dragan Marušič, D. W. Morris, Joy Morris, Primož Šparl, 2012, original scientific articleAbstract: We prove that if Cay▫$(G; S)$▫ is a connected Cayley graph with ▫$n$▫ vertices, and the prime factorization of ▫$n$▫ is very small, then Cay▫$(G; S)$▫ has a hamiltonian cycle. More precisely, if ▫$p$▫, ▫$q$▫, and ▫$r$▫ are distinct primes, then ▫$n$▫ can be of the form kp with ▫$24 \ne k < 32$▫, or of the form ▫$kpq$▫ with ▫$k \le 5$▫, or of the form ▫$pqr$▫, or of the form ▫$kp^2$▫ with ▫$k \le 4$▫, or of the form ▫$kp^3$▫ with ▫$k \le 2$▫.Found in: osebiKeywords: graph theory, Cayley graphs, hamiltonian cyclesPublished: 15.10.2013; Views: 1673; Downloads: 68 Full text (0,00 KB) 35.Algebraični aspekti teorije grafovAdemir Hujdurović, 2013, doctoral dissertationFound in: osebiKeywords: 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 groupPublished: 10.07.2015; Views: 1628; Downloads: 7 Full text (0,00 KB) 36.On the full automorphism group in vertex-transitive graphsDragan Marušič, 2015, published scientific conference contribution abstractFound in: osebiKeywords: odd automorphism, automorphism group, graphPublished: 15.10.2015; Views: 883; Downloads: 14 Full text (0,00 KB) 37.Reachability relations in digraphsNorbert Seifter, Boris Zgrablić, Aleksander Malnič, Primož Šparl, Dragan Marušič, 2008, original scientific articleAbstract: 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.Found in: osebiKeywords: graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growthPublished: 03.04.2017; Views: 943; Downloads: 91 Full text (0,00 KB) 38.On cyclic edge-connectivity of fullerenesDragan Marušič, Klavdija Kutnar, 2008, original scientific articleAbstract: A graph is said to be cyclically ▫$k$▫-edge-connected, if at least ▫$k$▫ edges must be removed to disconnect it into two components, each containing a cycle. Such a set of ▫$k$▫ edges is called a cyclic-k-edge cutset and it is called a trivial cyclic-k-edge cutset if at least one of the resulting two components induces a single ▫$k$▫-cycle. It is known that fullerenes, that is, 3-connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclically 5-edge-connected. In this article it is shown that a fullerene ▫$F$▫ containing a nontrivial cyclic-5-edge cutset admits two antipodal pentacaps, that is, two antipodal pentagonal faces whose neighboring faces are also pentagonal. Moreover, it is shown that ▫$F$▫ has a Hamilton cycle, and as a consequence at least ▫$15 \cdot 2^{n/20-1/2}$▫ perfect matchings, where ▫$n$▫ is the order of ▫$F$▫.Found in: osebiKeywords: graph, fullerene graph, cyclic edge-connectivity, hamilton cycle, perfect matchingPublished: 03.04.2017; Views: 755; Downloads: 92 Full text (0,00 KB) 39.Minimal normal subgroups of transitive permutation groups of square-free degreeAleksander Malnič, Dragan Marušič, Edward Dobson, Lewis A. Nowitz, 2007, original scientific articleAbstract: It is shown that a minimal normal subgroup of a transitive permutation group of square-free degree in its induced action is simple and quasiprimitive, with three exceptions related to ▫$A_5$▫, ▫$A_7$▫, and PSL(2,29). Moreover, it is shown that a minimal normal subgroup of a 2-closed permutation group of square-free degree in its induced action is simple. As an almost immediate consequence, it follows that a 2-closed transitive permutation group of square-free degree contains a semiregular element of prime order, thus giving a partial affirmative answer to the conjecture that all 2-closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs,Discrete Math. 36 (1981) 69-81; P.J. Cameron (Ed.), Problems from the fifteenth British combinatorial conference, Discrete Math. 167/168 (1997) 605-615]).Found in: osebiKeywords: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graphPublished: 03.04.2017; Views: 937; Downloads: 55 Full text (0,00 KB) 40.Symmetry structure of bicirculantsBoštjan Frelih, Primož Šparl, Aleksander Malnič, Dragan Marušič, 2007, original scientific articleAbstract: 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: osebiKeywords: mathematics, graph theory, graph, circulant, bicirculant, automorphism groupPublished: 03.04.2017; Views: 1047; Downloads: 59 Full text (0,00 KB)
Search done in 0 sec.