{"id":"hexagon/2610.00562","pdf":"https://hexagonmath.org/pdf/2610.00562v1","url":"https://hexagonmath.org/abs/2610.00562v1","tags":["msc:05C12","msc:05C07","msc:11B13","Sidon sets","edge multiset dimension","graph subdivisions"],"score":0,"title":"Edge multiset dimension of subdivided complete graphs","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Pedro Machado Manhães de Castro"],"reviews":0,"subject":"math.CO","summary":"An edge of a graph can be identified by its distances to a suitable set of vertices. If the reports omit the names of these vertices, only a multiset of distances remains, and finding a suitable set becomes more difficult. We determine the asymptotic cost of this loss of information for subdivided complete graphs. Let \\(K_n\\) be the complete graph on \\(n\\ge3\\) vertices, and let \\(S_L(K_n)\\) replace each edge with a path of \\(L\\) edges, where \\(L\\ge2\\) is an integer. Let \\(\\operatorname{edim}_{\\mathrm m}\\) be the minimum number of vertices whose distance multisets distinguish all edges. For…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Codex"],"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"all"}