21. The automorphism groups of non-edge transitive rose window graphsEdward Dobson, István Kovács, Štefko Miklavič, 2015, izvirni znanstveni članek Opis: In this paper, we determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we determine the isomorphism classes of non-edge-transitive rose window graphs. Ključne besede: rose window graphs, automorphism group, isomorphism problem, vertex-transitive graph Objavljeno v RUP: 30.12.2021; Ogledov: 1209; Prenosov: 22 Celotno besedilo (275,74 KB) |
22. Some recent discoveries about half-arc-transitive graphs : dedicated to Dragan Marušič on the occasion of his 60th birthdayMarston D. E. Conder, Primož Potočnik, Primož Šparl, 2015, izvirni znanstveni članek Opis: We present some new discoveries about graphs that are half-arc-transitive (that is, vertex- and edge-transitive but not arc-transitive). These include the recent discovery of the smallest half-arc-transitive 4-valent graph with vertex-stabiliser of order 4, and the smallest with vertex-stabiliser of order 8, two new half-arc-transitive 4-valent graphs with dihedral vertex-stabiliser ▫$D_4$▫ (of order 8), and the first known half-arc-transitive 4-valent graph with vertex-stabiliser of order 16 that is neither abelian nor dihedral. We also use half-arc-transitive group actions to provide an answer to a recent question of Delorme about 2-arc-transitive digraphs that are not isomorphic to their reverse. Ključne besede: graph, edge-transitive, vertex-transitive, arc-transitive, half arc-transitive Objavljeno v RUP: 30.12.2021; Ogledov: 1049; Prenosov: 17 Celotno besedilo (333,06 KB) |
23. Commuting graphs and extremal centralizersGregor Dolinar, Aleksandr Èmilevič Guterman, Bojan Kuzma, Polona Oblak, 2014, izvirni znanstveni članek Opis: We determine the conditions for matrix centralizers which can guarantee the connectedness of the commuting graph for the full matrix algebra ▫$M_n(\mathbb{F})$▫ over an arbitrary field ▫$\mathbb{F}$▫. It is known that if ▫$\mathbb{F}$▫ is an algebraically closed field and ▫$n \ge 3$▫, then the diameter of the commuting graph of ▫$M_n(\mathbb{F})$▫ is always equal to four. We construct a concrete example showing that if ▫$\mathbb{F}$▫ is not algebraically closed, then the commuting graph of ▫$M_n(\mathbb{F})$▫ can be connected with the diameter at least five. Ključne besede: commuting graph, matrix ring, centralizer Objavljeno v RUP: 30.12.2021; Ogledov: 1029; Prenosov: 24 Celotno besedilo (228,78 KB) |
24. Sectional split extensions arising from lifts of groupsRok Požar, 2013, izvirni znanstveni članek Opis: Covering techniques have recently emerged as an effective tool used for classification of several infinite families of connected symmetric graphs. One commonly encountered technique is based on the concept of lifting groups of automorphisms along regular covering projections ▫$\wp \colon \tilde{X} \to X$▫. Efficient computational methods are known for regular covers with cyclic or elementary abelian group of covering transformations CT▫$(\wp)$▫. In this paper we consider the lifting problem with an additional condition on how a group should lift: given a connected graph ▫$X$▫ and a group ▫$G$▫ of its automorphisms, find all connected regular covering projections ▫$\wp \colon \tilde{X} \to X$▫ along which ▫$G$▫ lifts as a sectional split extension. By this we mean that there exists a complement ▫$\overline{G}$▫ of CT▫$(\wp)$▫ within the lifted group ▫$\tilde{G}$▫ such that ▫$\overline{G}$▫ has an orbit intersecting each fibre in at most one vertex. As an application, all connected elementary abelian regular coverings of the complete graph ▫$K_4$▫ along which a cyclic group of order 4 lifts as a sectional split extension are constructed. Ključne besede: covering projection, graph, group extension, lifting automorphisms, voltage assignment Objavljeno v RUP: 30.12.2021; Ogledov: 1297; Prenosov: 4 Celotno besedilo (365,16 KB) |
25. Edge-contributions of some topological indices and arboreality of molecular graphsTomaž Pisanski, Janez Žerovnik, 2009, izvirni znanstveni članek Opis: Some graph invariants can be computed by summing certain values, called edge-contributions over all edges of graphs. In this note we use edge-contributions to study relationships among three graph invariants, also known as topological indices in mathematical chemistry: Wiener index, Szeged index and recently introduced revised Szeged index. We also use the quotient between the Wiener index and the revised Szeged index to study tree-likeness of graphs. Ključne besede: mathematical chemistry, chemical graph theory, topological index, revised Szeged index Objavljeno v RUP: 30.12.2021; Ogledov: 1240; Prenosov: 20 Celotno besedilo (158,93 KB) |
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28. Allocating indivisible items with minimum dissatisfaction on preference graphsNina Chiarelli, Clément Jean Dallard, Andreas Darmann, Stefan Lendl, Martin Milanič, Peter Muršič, Nevena Pivač, Ulrich Pferschy, 2021, objavljeni znanstveni prispevek na konferenci Ključne besede: fair division, partial order, preference graph Objavljeno v RUP: 29.10.2021; Ogledov: 1869; Prenosov: 23 Povezava na celotno besedilo |
29. Bonsma, Paul; Paulusma, Daniël: Using contracted solution graphs for solving reconfiguration problems. (English summary) Acta Inform. 56 (2019), no. 7-8, 619-648.Clément Jean Dallard, 2021, recenzija, prikaz knjige, kritika Ključne besede: reconfiguration, dynamic programming, graph coloring Objavljeno v RUP: 25.10.2021; Ogledov: 1599; Prenosov: 9 Povezava na celotno besedilo |
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