A vertex subset S of a graph G is a general position set of G if no vertex of S lies on a geodesic between two other vertices of S. The cardinality of a largest general position set of G is the general position number (gp-number) gp(G) of G. The gp-number is determined for some families of Kneser graphs, in particular for K(n, 2) and K(n, 3). A sharp lower bound on the gp-number is proved for Cartesian products of graphs. The gp-number is also determined for joins of graphs, coronas over graphs, and line graphs of complete graphs.

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.

No abstract

The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic; such sets are refereed to as gp-sets of G. A formula for the number of gp-sets in P r P s , r, s ≥ 2, is determined. The general position number of cylinders P r C s is deduced, while gp(C r C s ) is bounded from the below by 6, whenever r ≥ s = 4 and r ≥ 6. It is proved that gp(P ∞ P ∞ P ∞ ) ≥ 14. A probabilistic lower bound on the general position number of Hamming graphs and of Cartesian graph powers is also achieved.