Strong edge geodetic problem on complete multipartite graphs and some extremal graphs for the problemKlavžar, Sandi (Avtor) Zmazek, Eva (Avtor) strong edge geodetic problemcomplete multipartite graphedge-coloringCartesian product of graphsA set of vertices $X$ of a graph $G$ is a strong edge geodetic set if to any pair of vertices from $X$ we can assign one (or zero) shortest path between them such that every edge of $G$ is contained in at least one on these paths. The cardinality of a smallest strong edge geodetic set of $G$ is the strong edge geodetic number ${\rm sg_e}(G)$ of $G$. In this paper, the strong edge geodetic number of complete multipartite graphs is determined. Graphs $G$ with ${\rm sg_e}(G) = n(G)$ are characterized and ${\rm sg_e}$ is determined for Cartesian products $P_n\,\square\, K_m$. The latter result in particular corrects an error from the literature.20242024-02-19 13:09:01Članek v reviji154510UDK: 519.17ISSN pri članku: 1018-6301DOI: 10.1007/s41980-023-00849-6COBISS_ID: 183235331sl