{"paper":{"title":"Strong geodetic problem on Cartesian products of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sandi Klav\\v{z}ar, Vesna Ir\\v{s}i\\v{c}","submitted_at":"2017-08-08T09:16:52Z","abstract_excerpt":"The strong geodetic problem is a recent variation of the geodetic problem. For a graph $G$, its strong geodetic number ${\\rm sg}(G)$ is the cardinality of a smallest vertex subset $S$, such that each vertex of $G$ lies on a fixed shortest path between a pair of vertices from $S$. In this paper, the strong geodetic problem is studied on the Cartesian product of graphs. A general upper bound for ${\\rm sg}(G \\,\\square\\, H)$ is determined, as well as exact values for $K_m \\,\\square\\, K_n$, $K_{1, k} \\,\\square\\, P_l$, and certain prisms. Connections between the strong geodetic number of a graph and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02414","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}