20.500.12556/RUL-154510 Strong edge geodetic problem on complete multipartite graphs and some extremal graphs for the problem A 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. strong edge geodetic problem complete multipartite graph edge-coloring Cartesian product of graphs krepko povezavno-geodetski problem polni multipartitini graf barvanje povezav kartezični produkt grafov true false true Angleški jezik Slovenski jezik Članek v reviji 2024-02-19 13:09:01 2024-02-19 13:09:04 2024-05-14 03:49:31 0000-00-00 00:00:00 2024 0 0 13 str. iss. 1, art. 13 Vol. 50 Feb. 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 1018-6301 10.1007/s41980-023-00849-6 183235331 s41980-023-00849-6.pdf s41980-023-00849-6.pdf 1 403CE551BAC9C7C67036670CEF172D1B 4faf9e8ad6deacd56152a040b67f2816caf9da09617ee5b2407209accc66942f 6f0fcaff-10fb-11ef-adc7-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=183492 https://link.springer.com/article/10.1007/s41980-023-00849-6 1 ad9a7443-cf1f-11ee-9559-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=180979 Fakulteta za matematiko in fiziko 0 0 0