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31.
Some recent discoveries about half-arc-transitive graphs : dedicated to Dragan Marušič on the occasion of his 60th birthday
Marston 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: 31.12.2021; Ogledov: 384; Prenosov: 16
.pdf Polno besedilo (333,06 KB)

32.
A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two : dedicated to Dragan Marušič on the occasion of his 60th birthday
Primož Potočnik, Pablo Spiga, Gabriel Verret, 2015, izvirni znanstveni članek

Opis: A complete list of all connected arc-transitive asymmetric digraphs of in-valence and out-valence 2 on up to 1000 vertices is presented. As a byproduct, a complete list of all connected 4-valent graphs admitting a half-arc-transitive group of automorphisms on up to 1000 vertices is obtained. Several graph-theoretical properties of the elements of our census are calculated and discussed.
Ključne besede: graphs, digraphs, edge-transitive, vertex-transitive, arc-transitive, half arc-transitive
Objavljeno v RUP: 31.12.2021; Ogledov: 395; Prenosov: 16
.pdf Polno besedilo (370,47 KB)

33.
Reachability relations, transitive digraphs and groups
Aleksander Malnič, Primož Potočnik, Norbert Seifter, Primož Šparl, 2015, izvirni znanstveni članek

Opis: In [A. Malnič, D. Marušič, N. Seifter, P. Šparl and B. Zgrablič, Reachability relations in digraphs, Europ. J. Combin. 29 (2008), 1566-1581] it was shown that properties of digraphs such as growth, property ▫$\mathbf{Z}$▫, and number of ends are reflected by the properties of certain reachability relations defined on the vertices of the corresponding digraphs. In this paper we study these relations in connection with certain properties of automorphism groups of transitive digraphs. In particular, one of the main results shows that if atransitive digraph admits a nilpotent subgroup of automorphisms with finitely many orbits, then its nilpotency class and the number of orbits are closely related to particular properties of reachability relations defined on the digraphs in question. The obtained results have interesting implications for Cayley digraphs of certain types of groups such as torsion-free groups of polynomial growth.
Ključne besede: Cayley digraph, reachability relation
Objavljeno v RUP: 31.12.2021; Ogledov: 403; Prenosov: 16
.pdf Polno besedilo (311,92 KB)

34.
Commuting graphs and extremal centralizers
Gregor 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: 31.12.2021; Ogledov: 369; Prenosov: 21
.pdf Polno besedilo (228,78 KB)

35.
Sectional split extensions arising from lifts of groups
Rok 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: 31.12.2021; Ogledov: 368; Prenosov: 3
.pdf Polno besedilo (365,16 KB)

36.
A note on homomorphisms of matrix semigroup
Matjaž Omladič, Bojan Kuzma, 2013, izvirni znanstveni članek

Opis: Let ▫$\mathbb{F}$▫ be a field. We classify multiplicative maps from ▫${\mathcal M}_n(\mathbb{F})$▫ to ▫${\mathcal M}_{n \choose k}(\mathbb{F})$▫ which annihilate a zero matrix and map rank-▫$k$▫ matrix into a rank-one matrix.
Ključne besede: matrix semigroup, homomorphism, representation
Objavljeno v RUP: 31.12.2021; Ogledov: 332; Prenosov: 17
.pdf Polno besedilo (247,09 KB)

37.
Edge-contributions of some topological indices and arboreality of molecular graphs
Tomaž 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: 338; Prenosov: 14
.pdf Polno besedilo (158,93 KB)

38.
39.
Importance of culture for sustainable development
Mitja Bervar, Anita Trnavčevič, 2019, izvirni znanstveni članek

Ključne besede: sustainability, culture, social cohesion, intercultural dialogue, fourth pillar
Objavljeno v RUP: 22.12.2021; Ogledov: 439; Prenosov: 34
.pdf Polno besedilo (901,93 KB)

40.
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