20.500.12556/DiRROS-18275 General position polynomials 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 $\sum_{i \geq 0} a_i x^i$, where $a_i$ 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. general position set general position number general position polynomial unimodality trees Cartesian product of graphs Kneser graphs množice v splošni legi število splošne lege polinom splošne lege unimodalnost drevesa kartezični produkt grafov Kneserjevi grafi true false true Angleški jezik Slovenski jezik Neznano 2024-02-28 10:13:51 2024-02-28 10:13:51 2024-03-07 12:48:31 0000-00-00 00:00:00 2024 0 0 16 str. iss. 3, [article no.] 110 Vol. 79 May 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2024-05-01 519.17 1422-6383 10.1007/s00025-024-02133-3 187024387 https://link.springer.com/article/10.1007/s00025-024-02133-3 1 4f448702-d611-11ee-900a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24818 s00025-024-02133-3.pdf s00025-024-02133-3.pdf 1 C344F14A1F3E3CDD2E3D55BB1B2CC4DC 1ca7b1e56575ff07324bc66c88291536703e2abca434e1108e0f73286186bdd9 baeb34c0-d611-11ee-900a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=24819 Inštitut za matematiko, fiziko in mehaniko 0 0 0