31. Polycyclic geometric realizations of the Gray configurationLeah Berman, Gábor Gévay, Tomaž Pisanski, 2025, izvirni znanstveni članek Opis: The Gray configuration is a (27_3) configuration which typically is realized as the points and lines of the 3×3×3 integer lattice. It occurs as a member of an infinite family of configurations defined by Bouwer in 1972. Since their discovery, both the Gray configuration and its Levi graph (i.e., its point-line incidence graph) have been the subject of intensive study. Its automorphism group contains cyclic subgroups isomorphic to Z3 and Z9, so it is natural to ask whether the Gray configuration can be realized in the plane with any of the corresponding rotational symmetry. In this paper, we show that there are two distinct polycyclic realizations with Z3 symmetry. In contrast, the only geometric polycyclic realization with straight lines and Z9 symmetry is only a “weak” realization, with extra unwanted incidences (in particular, the realization is actually a (27_4) configuration).
Ključne besede: Gray graph, Gray configuration, polycirculant, polycyclic configuration
Objavljeno v RUP: 29.09.2025; Ogledov: 430; Prenosov: 4
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32. On commutative association schemes and associated (directed) graphsGiusy Monzillo, Safet Penjić, 2025, izvirni znanstveni članek Opis: Let ${\mathcal M}$ denote the Bose--Mesner algebra of a commutative $d$-class association scheme ${\mathfrak X}$ (not necessarily symmetric), and $\Gamma$ denote a (strongly) connected (directed) graph with adjacency matrix $A$. Under the assumption that $A$ belongs to ${\mathcal M}$, we describe the combinatorial structure of $\Gamma$. Moreover, we provide an algebraic-combinatorial characterization of $\Gamma$ when $A$ generates ${\mathcal M}$. Among else, we show that, if ${\mathfrak X}$ is a commutative $3$-class association scheme that is not an amorphic symmetric scheme, then we can always find a (directed) graph $\Gamma$ such that the adjacency matrix $A$ of $\Gamma$ generates the Bose--Mesner algebra ${\mathcal M}$ of ${\mathfrak X}$.
Ključne besede: commutative association schemes, association schemes, Bose-Mesner algebra, equitable partition, graphs generating schemes, quotient-polynomial graphs, x-distance-faithful intersection diagram
Objavljeno v RUP: 26.09.2025; Ogledov: 334; Prenosov: 4
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33. Conformal hypergraphs : duality and implications for the upper clique transversal problemEndre Boros, Vladimir Gurvich, Martin Milanič, Yushi Uno, 2025, izvirni znanstveni članek Opis: Given a hypergraph H, the dual hypergraph of H is the hypergraph of all minimal transversals of H. The dual hypergraph is always Sperner, that is, no hyperedge contains another. A special case of Sperner hypergraphs are the conformal Sperner hypergraphs, which correspond to the families of maximal cliques of graphs. All these notions play an important role in many fields of mathematics and computer science, including combinatorics, algebra, database theory, etc. In this paper we study conformality of dual hypergraphs and prove several results related to the problem of recognizing this property. In particular, we show that the problem is in co-NP and can be solved in polynomial time for hypergraphs of bounded dimension. In the special case of dimension 3, we reduce the problem to 2-Satisfiability. Our approach has an implication in algorithmic graph theory: we obtain a polynomial-time algorithm for recognizing graphs in which all minimal transversals of maximal cliques have size at most k, for any fixed k.
Ključne besede: conformal hypergraph, dual hypergraph, hypergraph, maximal clique, upper clique transversal
Objavljeno v RUP: 25.09.2025; Ogledov: 345; Prenosov: 4
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34. Self-compassion around the world : measurement invariance of the Short form of the self-compassion scale (SCS-SF) across 65 nations, 40 languages, gender identities, and age groupsViren Swami, Ulrich S. Tran, Martin Voracek, Toivo Aavik, Hamed Abdollahpour Ranjbar, Sulaiman Olanrewaju Adebayo, Reza Afhami, Oli Ahmed, Annie Aimé, Marwan Akel, Mirjam Koprivnik, Vita Poštuvan, 2025, izvirni znanstveni članek Opis: Objectives The 12-item Self-Compassion Scale–Short Form (SCS–SF) is a widely used instrument for the assessment of self-compassion. To date, there have been few examinations of this instrument’s psychometric properties, particularly across nations and languages. Therefore, we used data from the Body Image in Nature Survey (BINS) to assess measurement invari- ance of the SCS–SF across nations, languages, gender identities, and age groups. Methods Participants (N = 56,968) from 65 nations completed the SCS–SF in 40 languages. Using these data, we tested various hypothesised models of the SCS–SF in the total sample and, using multi-group confirmatory factor analysis, tested for invariance of the optimal model across national groups, languages, gender identities, and age groups. Results In the total dataset, we found that an 11-item, 2-factor model (i.e., SCS-11) provided best fit to the data, with the two factors tapping distinct constructs of compassionate and uncompassionate self-responding. The SCS-11 was found to be partially scalar invariant across national groups and languages, and fully scalar invariant across gender identities and age groups. There was wide variation in latent means for the two factors, particularly across national groups and languages. Further analyses showed negligible associations between the two factors and sociodemographic variables, including marital status, financial security, and urbanicity. Conclusions Our results suggest that it may be possible to derive a stable 2-factor model of the SCS–SF for use in cross- cultural research, but also highlight the likelihood of cross-national and cross-linguistic variations in the way that self- compassion is understood.
Ključne besede: Self-compassion scale - short form (SCS–SF), 65 nations, 40 languages
Objavljeno v RUP: 12.09.2025; Ogledov: 414; Prenosov: 3
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35. Photochemical behavior of colloidal lignin particles under controlled UV exposure : balancing self-stabilization and degradationJulia Tomasich, Rene Alexander Herrera Diaz, Anna Malgorzata Sandak, Michael Harasek, Stefan Beisl, Oihana Gordobil, 2025, izvirni znanstveni članek Opis: Colloidal Lignin Particles (CLPs), with their polyphenolic structure, are promising sustainable alternatives to chemical UV filters. This study investigates the photochemical behavior of CLPs under ultraviolet irradiation synthetized from five different technical raw lignins (Alkali, Organosolv, two Enzymatic Hydrolyzed and Softwood Kraft Lignin) via solvent-shift procedure. The suspensions were irradiated using a self-developed UV-pen set-up and a commercially available UV chamber, enabling controlled UV exposure over time. Variations in the physicochemical properties of irradiated colloidal lignin particles were characterized by Multi-Angle Dynamic Light Scattering (MADLS), Fourier Transform Infrared Spectroscopy (FTIR) coupled with chemometrics, UV–Vis spectroscopy, and High-Performance Size Exclusion Chromatography (HP-SEC). CLPs exhibited comparable responses after 14 days of UV exposure, with alterations in particle chemistry, particularly in the formation of new functional groups and molecular rearrangement. Moreover, the photochemical stability of CLPs was found to be highly dependent on both their concentration and the nature of the dispersion medium (aqueous, hexane-based, and solid-state). At higher concentrations (1.8 mg/mL), CLPs demonstrated effective self-stabilization, while lower concentrations led to rapid degradation, resulting in the disappearance of particles and the formation of low-molecular-weight fragments. Additionally, Minimal photochemical changes were observed in non-aqueous or solid-state environments due to restricted molecular mobility. These findings provide valuable insights into the degradation pathways and stability across different environmental contexts, which can contribute to understanding the potential environmental impact of CLPs in aquatic ecosystems.
Ključne besede: biobased materials, lignin colloidal particles, photodegradation, UV-irradiation, spectroscopy
Objavljeno v RUP: 09.09.2025; Ogledov: 426; Prenosov: 4
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36. On reduced Hamilton walksAleksander Malnič, Rok Požar, 2026, izvirni znanstveni članek Opis: A Hamilton walk in a finite graph is a walk, either open or closed, that traverses every vertex at least once. Here, we introduce Hamilton walks that are reduced in the sense that they avoid immediate backtracking: a reduced Hamilton walk never traverses the same edge forth and back consecutively. While every connected graph admits a Hamilton walk, existence of a reduced Hamilton walk is not guaranteed for all graphs. However, we prove that a reduced Hamilton walk does exist in a connected graph with minimal valency at least 2. Furthermore, given such a graph on n vertices, we present an O(n2)-time algorithm that constructs a reduced Hamilton walk of length at most n(n+3)/2. Specifically, for a graph belonging to a family of regular expander graphs, we can find a reduced Hamilton walk of length at most c(6n−2)logn+2n, where c is a constant independent of n.
Ključne besede: algorithm, Hamilton walk, nonstandard metric, reduced walk
Objavljeno v RUP: 09.09.2025; Ogledov: 474; Prenosov: 7
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37. Modelling the spread of infectious diseases in public transport systems under varying demand patterns and capacity constraintsLászló Hajdu, Jovan Pavlović, Miklós Ferenz Krész, András Bóta, 2025, izvirni znanstveni članek Opis: Understanding the dynamics of passenger interactions and their epidemiological impact across public transportation systems is crucial for both service efficiency and public health. High passenger density and close physical proximity have been shown to accelerate the spread of infectious diseases. During the COVID-19 pandemic, many public transportation companies took measures to slow down and minimize the spread of the disease. One of these measures was introducing spacing and capacity constraints on public transit vehicles. Our objective is to explore the effects of changes in demand and transportation measures from an epidemiological point of view, offering alternative measures to public transportation companies to keep the system operational while minimizing the epidemiological risk as much as possible. Our findings show that restricting vehicle capacity can significantly reduce the spread of infections, while demand-related measures have an even stronger effect. Combining these approaches offers the best solutions for balancing public health and operability.
Ključne besede: agent based modelling, infectious diseases, network analysis
Objavljeno v RUP: 27.08.2025; Ogledov: 505; Prenosov: 3
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38. On cubic vertex-transitive graphs of given girthEdward Tauscher Dobson, Ademir Hujdurović, Wilfried Imrich, Ronald Ortner, 2025, izvirni znanstveni članek Opis: A set of vertices of a graph is distinguishing if the only automorphism that preserves it is the identity. The minimal size of such sets, if they exist, is the distinguishing cost. The distinguishing costs of vertex transitive cubic graphs are well known if they are 1-arc-transitive, or if they have two edge orbits and either have girth 3 or vertex-stabilizers of order 1 or 2. There are many results about vertex-transitive cubic graphs of girth 4 with two edge orbits, but for larger girth almost nothing is known about the distinguishing costs of such graphs. We prove that cubic vertex-transitive graphs of girth 5 with two edge orbits have distinguishing cost 2, and prove the non-existence of infinite 3-arc-transitive cubic graphs of girth 6.
Ključne besede: distinguishing number, distinguishing cost, vertex-transitive cubic graphs, automorphisms
Objavljeno v RUP: 27.08.2025; Ogledov: 697; Prenosov: 4
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39. Homomorphisms from the Coxeter graphMarko Orel, Draženka Višnjić, 2025, izvirni znanstveni članek Opis: Let $S_n(\mathbb{F}_2)$ be the set of all $n\times n$ symmetric matrices with coefficients in the binary field $\mathbb{F}_2=\{0,1\}$, and let $SGL_n(\mathbb{F}_2)$ be its subset formed by invertible matrices. Let $\widehat{\Gamma}_n$ be the graph with the vertex set $S_n(\mathbb{F}_2)$ where a pair of vertices $\{A,B\}$ form an edge if and only if $rank(A-B)=1$. Similarly, let $\Gamma_n$ be the subgraph in $\widehat{\Gamma}_n$, which is induced by the set $SGL_n(\mathbb{F}_2)$. Graph $\Gamma_n$ generalizes the well-known Coxeter graph, which is isomorphic to $\Gamma_3$. Motivated by research topics in coding theory, matrix theory, and graph theory, this paper represents the first step towards the characterization of all graph homomorphisms $\Phi: \Gamma_n\to \widehat{\Gamma}_m$ where $n,m$ are positive integers. Here, the case $n=3$ is solved.
Ključne besede: preserver problems, symmetric matrices, invertible matrices, binary field, rank, graph homomorphisms, Coxeter graph
Objavljeno v RUP: 27.08.2025; Ogledov: 475; Prenosov: 5
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40. Risk of job loss during the COVID-19 pandemic predicts anxiety in womenNina Krohne, Tina Podlogar, Vanja Gomboc, Meta Lavrič, Nuša Zadravec Šedivy, Diego De Leo, Vita Poštuvan, 2025, izvirni znanstveni članek Opis: Background and Objective: During the COVID-19 pandemic, women faced unique employment-related stressors, including higher exposure to unstable working conditions, increased workload changes due to motherhood, and greater risk of infection in certain jobs. This study explores how these factors influence women’s anxiety and subjective well-being, aiming to identify vulnerable groups. Materials and Methods: 230 employed Slovene women, aged from 19 to 64 years (M = 32.60, SD = 10.41), participated in an online survey containing a State-Trait Anxiety Inventory (STAI-6), WHO-5 Well-being Index, and a set of questions regarding their occupation and demographic profile. Hierarchical linear regressions and chi-squared tests were performed. Results: The risk of job or income loss significantly predicted an increase in anxiety levels. However, despite fear of infection, none of the work-related variables predicted a significant decrease in subjective well-being. Women reporting risk of job or income loss are predominantly those with lower education and income, working students, self-employed, or working in the private sector. Conclusions: Employment insecurity is an important contributor to anxiety in women. The findings highlight the need to ensure job security, particularly for women working in precariat working conditions, as their work and economic stability prove to be vulnerable to external economic disturbances.
Ključne besede: COVID-19, women, employment insecurity, anxiety, mental health
Objavljeno v RUP: 08.08.2025; Ogledov: 543; Prenosov: 6
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