{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:29:22Z","timestamp":1753882162004,"version":"3.41.2"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:p> A proper vertex coloring of a graph [Formula: see text] is equitable if the sizes of any two color classes differ by at most one. The equitable chromatic number of a graph [Formula: see text], denoted by [Formula: see text], is the minimum [Formula: see text] such that [Formula: see text] is equitably [Formula: see text]-colorable. In this paper, we discuss some basic properties of equitable critical graphs as well as equitable [Formula: see text]-critical graphs. A graph [Formula: see text] is called equitable critical if [Formula: see text] for every proper subgraph [Formula: see text] of [Formula: see text]. [Formula: see text] is called equitable [Formula: see text]-critical if it is equitable [Formula: see text]-chromatic and equitable critical. <\/jats:p><jats:p> Furthermore, we discuss that equitable vertex (edge) critical, equitable critical vertex (edge) graphs. <\/jats:p>","DOI":"10.1142\/s1793830922501683","type":"journal-article","created":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T13:45:15Z","timestamp":1668519915000},"source":"Crossref","is-referenced-by-count":0,"title":["Equitable critical graphs"],"prefix":"10.1142","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3840-2174","authenticated-orcid":false,"given":"Loura","family":"Jency","sequence":"first","affiliation":[{"name":"PG and Research Department of Mathematics, Loyola College, Chennai 600 034, India"}]},{"given":"Benedict Michael","family":"Raj","sequence":"additional","affiliation":[{"name":"PG and Research Department of Mathematics, St. Joseph\u2019s College (Affiliated to Bharathidasan University), Trichy 620 002, India"}]}],"member":"219","published-online":{"date-parts":[[2022,11,15]]},"reference":[{"key":"S1793830922501683BIB001","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.endm.2009.03.001","volume":"33","author":"Ali A.","year":"2009","journal-title":"Electron. 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