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If [Formula: see text] is obtained by attaching whiskers at some vertices of the cycle of length [Formula: see text], then we show that [Formula: see text]. Furthermore, we characterize [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text]. In each of these cases, we classify the uniqueness of the extremal Betti number of these graphs. <\/jats:p>","DOI":"10.1142\/s0218196721500466","type":"journal-article","created":{"date-parts":[[2021,7,8]],"date-time":"2021-07-08T09:57:46Z","timestamp":1625738266000},"page":"1293-1318","source":"Crossref","is-referenced-by-count":3,"title":["Binomial edge ideals of unicyclic graphs"],"prefix":"10.1142","volume":"31","author":[{"given":"Rajib","family":"Sarkar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,7,7]]},"reference":[{"key":"S0218196721500466BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s13348-019-00268-z"},{"key":"S0218196721500466BIB002","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/13241"},{"key":"S0218196721500466BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2017.11.004"},{"key":"S0218196721500466BIB004","series-title":"Cambridge Studies in Advanced Mathematics","volume-title":"Cohen\u2013Macaulay Rings","volume":"39","author":"Bruns W.","year":"1993"},{"issue":"2","key":"S0218196721500466BIB005","first-page":"149","volume":"24","author":"Chaudhry F.","year":"2016","journal-title":"An. \u015etiin\u0163. 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