Ambhore, Siddhi BaluSiddhi BaluAmbhoreSaha, KamaleshKamaleshSahaSengupta, IndranathIndranathSengupta2025-08-312025-08-312024-12-0110.1007/s40306-024-00540-w2-s2.0-85197930667https://d8.irins.org/handle/IITG2025/28614The invariant v-number was introduced very recently in the study of Reed-Muller-type codes. Jaramillo and Villarreal (J. Combin. Theory Ser. A 177:105310, 2021) initiated the study of the v-number of edge ideals. Inspired by their work, we take the initiation to study the v-number of binomial edge ideals in this paper. We discuss some properties and bounds of the v-number of binomial edge ideals. We explicitly find the v-number of binomial edge ideals locally at the associated prime corresponding to the cutset ∅. We show that the v-number of Knutson binomial edge ideals is less than or equal to the v-number of their initial ideals. Also, we classify all binomial edge ideals whose v-number is 1. Moreover, we try to relate the v-number with the Castelnuvo-Mumford regularity of binomial edge ideals and give a conjecture in this direction.falseBinomial edge ideals | Castelnuovo-Mumford regularity | Completion set | Initial ideals | v-numberArticle23154144611-628December 20244arJournal5