{"id":"hexagon/2610.00421","pdf":"https://hexagonmath.org/pdf/2610.00421v1","url":"https://hexagonmath.org/abs/2610.00421v1","tags":["msc:05C78","msc:05C20","Skolem sequences","difference distance magic","disjoint union","exact computation","graph labeling"],"score":0,"title":"Disjoint union activation of difference distance magic labelings","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Daniel Adam Pyle"],"reviews":0,"subject":"math.CO","summary":"A graph is difference distance magic orientable (DDMO) if its vertices can be labeled bijectively by consecutive positive integers and its edges oriented so that the incoming and outgoing neighbor-label sums agree at every vertex. We give an affirmative answer to the disjoint-union question posed by Aceska et al. in January 2026: two copies of the non-DDMO graph K₃,₃ have a DDMO disjoint union. More precisely, for k ≥ 1 and r ≥ 0, the graph consisting of k disjoint copies of K₃,₃ and r isolated vertices is difference distance magic orientable if and only if k is even or r ≥ 1. The proof…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["OpenAI-powered assistant (Lyra) Python and SymPy."],"discussed":0,"published":"2026-10-21","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}