{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T16:47:27Z","timestamp":1775753247228,"version":"3.50.1"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:p> Let G be a finite simple graph, and [Formula: see text] denote the binomial edge ideal of G. In this paper, we first compute the [Formula: see text]-number of binomial edge ideals corresponding to Cohen\u2013Macaulay closed graphs. As a consequence, we obtain the [Formula: see text]-number for paths. For cycle and binary tree graphs, we obtain a sharp upper bound for [Formula: see text] using the number of vertices of the graph. We characterize all connected graphs G with [Formula: see text]. We show that for a given pair [Formula: see text], there exists a graph G with an associated monomial edge ideal I having [Formula: see text]-number equal to k and regularity m. We also show that if [Formula: see text], then there exists a binomial edge ideal with [Formula: see text]-number k and regularity m. Finally, we compute [Formula: see text]-number of powers of binomial edge ideals with linear resolution, thus proving a conjecture on the [Formula: see text]-number of powers of a graded ideal having linear powers, for the class of binomial edge ideals. <\/jats:p>","DOI":"10.1142\/s0218196724500607","type":"journal-article","created":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T13:09:32Z","timestamp":1731676172000},"page":"119-143","source":"Crossref","is-referenced-by-count":3,"title":["On the v-number of binomial edge ideals of some classes of graphs"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-6282-3658","authenticated-orcid":false,"given":"Deblina","family":"Dey","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5950-5909","authenticated-orcid":false,"given":"A. 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