1. Maximizing Nursing Students’ Engagement in Distance Learning: Strategies and InsightsBoris Ilić, Irena Kovačević, Danko Relić, Vesna Švab, Vedrana Vejzović, Seher Yurt, 2025, independent scientific component part or a chapter in a monograph Abstract: The increase of online nursing education, driven by technology and the demand for flexible learning, has emphasized the importance of student engagement. Participation plays a key role in shaping both academic achievement and the acquisition of crucial nursing skills. This chapter explores the impact of technological factors such as audio and video quality, as well as internet speed, on student engagement. Moreover, it delves into how the ERR framework – a teaching approach that includes Evocation, Realization of Meaning and Reflection, along with other interactive tools can be used in online learning settings to improve nursing students’ participation. This work aims to provide educators with practical insights for improving online nursing education by combining technological considerations with innovative teaching strategies.
Keywords: nursing education, distance learning, student engagement, ERR framework, Technological factors
Published in RUP: 22.12.2025; Views: 185; Downloads: 1
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2. A classification of Q-polynomial distance-regular graphs with girth 6Štefko Miklavič, 2025, original scientific article Abstract: Let Γ denote a Q-polynomial distance-regular graph with diameter D and valency k≥3. In [Homotopy in Q-polynomial distance-regular graphs, Discrete Math., {\bf 223} (2000), 189–206], H. Lewis showed that the girth of Γ is at most 6. In this paper we classify graphs that attain this upper bound. We show that Γ has girth 6 if and only if it is either isomorphic to the Odd graph on a set of cardinality 2D+1, or to a generalized hexagon of order (1,k−1).
Keywords: distance-regular graphs, Q-polynomial property, girth
Published in RUP: 01.12.2025; Views: 1164; Downloads: 3
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3. On distance preserving and sequentially distance preserving graphsJason P. Smith, Emad Zahedi, 2025, original scientific article Abstract: A graph H is an isometric subgraph of G if d_H(u,v)=d_G(u,v), for every pair u,v ∈ V(H). A graph is distance preserving if it has an isometric subgraph of every possible order. A graph is sequentially distance preserving if its vertices can be ordered such that deleting the first i vertices results in an isometric subgraph, for all i≥1. We give an equivalent condition to sequentially distance preserving based upon simplicial orderings. Using this condition, we prove that if a graph does not contain any induced cycles of length 5 or greater, then it is sequentially distance preserving and thus distance preserving. Next we consider the distance preserving property on graphs with a cut vertex. Finally, we define a family of non-distance preserving graphs constructed from cycles.
Keywords: distance preserving, isometric subgraph, sequentially distance preserving, chordal, cut vertex, simplicial vertex
Published in RUP: 03.11.2025; Views: 377; Downloads: 1
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4. Distance-regular Cayley graphs over ℤpˢ ⊕ ℤpXiongfeng Zhan, Lu Lu, Xueyi Huang, 2025, original scientific article Abstract: In 2007, Miklavič and Potočnik proposed the problem of characterizing distance-regular Cayley graphs, which can be viewed as an extension of the problem of identifying strongly regular Cayley graphs, or equivalently, regular partial difference sets. Let p be an odd prime. In this paper, all distance-regular Cayley graphs over ℤps ⊕ ℤp are identified. It is shown that every such graph is isomorphic to a complete graph, a complete multipartite graph, or the line graph of a transversal design TD(r, p) with 2 ≤ r ≤ p − 1.
Keywords: distance-regular graph, Cayley graph, Schur ring, Fourier transformation, transversal design
Published in RUP: 21.10.2025; Views: 383; Downloads: 2
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5. On commutative association schemes and associated (directed) graphsGiusy Monzillo, Safet Penjić, 2025, original scientific article Abstract: 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 ${\mathfrak X}$.
Keywords: commutative association schemes, association schemes, Bose-Mesner algebra, equitable partition, graphs generating schemes, quotient-polynomial graphs, x-distance-faithful intersection diagram
Published in RUP: 26.09.2025; Views: 352; Downloads: 4
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6. The Gray graph is a unit-distance graphLeah Berman, Gábor Gévay, Tomaž Pisanski, 2025, original scientific article Abstract: In this note we give a construction proving that the Gray graph, which is the smallestcubic semisymmetric graph, is a unit-distance graph.
Keywords: polycirculant, unit-distance graph, Gray graph, ADAM graph, generalized Petersen graph
Published in RUP: 10.09.2025; Views: 588; Downloads: 5
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7. Tetravalent distance magic graphs of small order and an infinite family of examplesKsenija Rozman, Primož Šparl, 2025, original scientific article Abstract: A graph of order ▫$n$▫ is distance magic if it admits a bijective labeling of its vertices with integers from ▫$1$▫ to ▫$n$▫ such that each vertex has the same sum of the labels of its neighbors. This paper contributes to the long term project of characterizing all tetravalent distance magic graphs. With the help of a computer we find that out of almost nine million connected tetravalent graphs up to order 16 only nine are distance magic. In fact, besides the six well known wreath graphs there are only three other examples, one of each of the orders 12, 14 and 16. We introduce a generalization of wreath graphs, the so-called quasi wreath graphs, and classify all distance magic graphs among them. This way we obtain infinitely many new tetravalent distance magic graphs. Moreover, the two non-wreath graphs of orders 12 and 14 are quasi wreath graphs while the one of order 16 can be obtained from a quasi wreath graph of order 14 using a simple construction due to Kovář, Fronček and Kovářová.
Keywords: distance magic, tetravalent, quasi wreath graph
Published in RUP: 10.09.2025; Views: 432; Downloads: 11
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8. The distance function on Coxeter-like graphs and self-dual codesMarko Orel, Draženka Višnjić, 2025, original scientific article Keywords: Coxeter graph, invertible symmetric matrices, binary field, rank, distance in graphs, alternate matrices, self-dual codes
Published in RUP: 30.05.2025; Views: 842; Downloads: 18
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9. Selected topics on Wiener indexMartin Knor, Riste Škrekovski, Aleksandra Tepeh, 2024, original scientific article Keywords: graph distance, Wiener index, average distance, topological index, molecular descriptor, chemical graph theory
Published in RUP: 26.05.2025; Views: 801; Downloads: 7
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