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In this paper, we give a criterion for the existence of tight toughness, isolated toughness and binding number bounds in a graph of a strong [Formula: see text]-star factor, [Formula: see text]-factor and [Formula: see text]-star factor. Moreover, we show that the bounds of the sufficient conditions are sharp. <\/jats:p>","DOI":"10.1142\/s0219265923500329","type":"journal-article","created":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T03:26:40Z","timestamp":1704857200000},"source":"Crossref","is-referenced-by-count":0,"title":["Bounds of Two Toughnesses and Binding Numbers for Star Factors"],"prefix":"10.1142","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2140-3438","authenticated-orcid":false,"given":"Yujia","family":"Gao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, P. R. 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