The general position number $$\mathrm{gp}(G)$$gp(G) of a connected graphGis the cardinality of a largest setSof vertices such that no three distinct vertices fromSlie on a common geodesic; such sets are refereed to as gp-sets ofG. The general position number of cylinders $$P_r\,\square \,C_s$$Pr□Cs is deduced. It is proved that $$\mathrm{gp}(C_r\,\square \,C_s)\in \{6,7\}$$gp(Cr□Cs)∈{6,7} whenever $$r\ge s \ge 3$$r≥s≥3 , $$s\ne 4$$s≠4 , and $$r\ge 6$$r≥6 . A probabilistic lower bound on the general position number of Cartesian graph powers is achieved. Along the way a formula for the number of gp-sets in $$P_r\,\square \,P_s$$Pr□Ps , where $$r,s\ge 2$$r,s≥2 , is also determined.

The paper aims to investigate the main factors influencing the mathematics achievement of social sciences university students in Slovenia. A conceptual model was derived where three categories of variables were taken into account: attitude towards mathematics and math anxiety, engagement in learning activities, and attitude towards involving technology in learning mathematics. Data were collected for seven consecutive academic years and analysed using Structural Equation Modelling (SEM). The results showed a very high coefficient of determination for mathematics achievement (0.801), indicating that variables “Perceived Level of Math Anxiety”, “Self-Engagement in Mathematics Course at University”, and “Perceived Usefulness of Technology in Learning Mathematics”, together, explain 80.1% of the total variance. Based on our findings, we can conclude that teaching in secondary school is a crucial determinant for success in mathematics at university. It is essential to identify the best methods for secondary school math teachers which will help them give future students better entry-level knowledge for universities. These methods will, hopefully, also improve the level of mathematics self-confidence, as well as lower the level of math anxiety, which all considerably affect the performance of students in university mathematics.

A subset of vertices of a graph G is a general position set if no triple of vertices from the set lie on a common shortest path in G. In this paper we introduce the general position polynomial as $$\sum _{i \ge 0} a_i x^i$$∑ i ≥ 0 a i x i , where $$a_i$$a i is the number of distinct general position sets of G with cardinality i. The polynomial is considered for several well-known classes of graphs and graph operations. It is shown that the polynomial is not unimodal in general, not even on trees. On the other hand, several classes of graphs, including Kneser graphs K(n, 2), with unimodal general position polynomials are presented.

This study examines the effects of COVID-19-related measures on the mathematics achievement of university students in social sciences in Slovenia. Our particular concern was to compare two student populations (pre-pandemic and pandemic) in terms of factors affecting student performance in mathematics courses. Data were collected over nine consecutive academic years (from 2013–2014 to 2020–2021) and analyzed using two-stage structural equation modelling (SEM). The analyses confirmed that the conceptual model developed before the pandemic was applicable during the pandemic period. For both populations (pre-pandemic and pandemic), mathematics confidence, perceived level of math anxiety, background knowledge from secondary school, and self-engagement in mathematics courses at university were confirmed as factors influencing mathematics achievement. Moreover, both populations perceived the effects of the factors in the same way, and the magnitude of the effects is comparable. The rather high values of determination coefficient for mathematics achievement (greater than 0.66 for both student populations) indicate that the variables “Perceived Level of Math Anxiety” and “Self-Engagement in Mathematics Course at University” together explain a significant proportion of the total variance before and during the pandemic. Consequently, the results of our case study indicated that pandemic measures did not have a significant impact on our students’ mathematics achievement. Although a more in-depth study of a broader sample of academic courses would be needed to confirm our findings, our experience indicates that mathematics courses at the tertiary level of education can be successfully delivered online.

Weighted Padovan graphs $Φ^{n}_{k}$, $n \geq 1$, $\lfloor \frac{n}{2} \rfloor \leq k \leq \lfloor \frac{2n-2}{3} \rfloor$, are introduced as the graphs whose vertices are all Padovan words of length $n$ with $k$ $1$s, two vertices being adjacent if one can be obtained from the other by replacing exactly one $01$ with a $10$. By definition, $\sum_k |V(Φ^{n}_{k})|=P_{n+2}$, where $P_n$ is the $n$th Padovan number. Two families of graphs isomorphic to weighted Padovan graphs are presented. The order, the size, the degree, the diameter, the cube polynomial, and the automorphism group of weighted Padovan graphs are determined. It is also proved that they are median graphs.