{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:16:42Z","timestamp":1753885002023,"version":"3.41.2"},"reference-count":5,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,10]]},"abstract":"<jats:p> The eccentric graph of a graph [Formula: see text], denoted by [Formula: see text], is a derived graph with the vertex set same as that of [Formula: see text] and two vertices in [Formula: see text] are adjacent if one of them is an eccentric vertex of the other. The process of constructing iterative eccentric graphs, denoted by [Formula: see text] is called eccentrication. A graph [Formula: see text] is said to be [Formula: see text] if [Formula: see text] are the only non-isomorphic graphs, and the graph [Formula: see text] is isomorphic to [Formula: see text]. In this paper, we prove the existence of an [Formula: see text]-cycle for any simple graph. The importance of this result lies in the fact that the enumeration of eccentrication of a graph reduces to a finite problem. Furthermore, the enumeration of a corresponding sequence of graph parameters such as chromatic number, domination number, independence number, minimum and maximum degree, etc., reduces to a finite problem. <\/jats:p>","DOI":"10.1142\/s1793830922501555","type":"journal-article","created":{"date-parts":[[2022,9,2]],"date-time":"2022-09-02T03:02:17Z","timestamp":1662087737000},"source":"Crossref","is-referenced-by-count":0,"title":["Cyclic property of iterative eccentrication of a graph"],"prefix":"10.1142","volume":"15","author":[{"given":"Manakkulam Rohith","family":"Raja","sequence":"first","affiliation":[{"name":"Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka 560029, India"}]},{"given":"Johan","family":"Kok","sequence":"additional","affiliation":[{"name":"Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka 560029, India"}]},{"given":"Tabitha Agnes","family":"Mangam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka 560029, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9692-4053","authenticated-orcid":false,"given":"Sudev","family":"Naduvath","sequence":"additional","affiliation":[{"name":"Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka 560029, India"}]}],"member":"219","published-online":{"date-parts":[[2022,9,30]]},"reference":[{"issue":"1","key":"S1793830922501555BIB001","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0012-365X(85)90188-8","volume":"56","author":"Akiyama J.","year":"1965","journal-title":"Discrete Math."},{"volume-title":"Graph Theory","year":"2001","author":"Harary F.","key":"S1793830922501555BIB002"},{"issue":"2","key":"S1793830922501555BIB003","first-page":"193","volume":"7","author":"Raja M. R.","year":"2022","journal-title":"Commun. Combin. Opt."},{"volume-title":"The Encyclopedia of Integer Sequences","year":"1995","author":"Sloane N. J. A.","key":"S1793830922501555BIB005"},{"key":"S1793830922501555BIB006","volume-title":"Introduction to Graph Theory","volume":"2","author":"West D. B.","year":"2001"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922501555","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,21]],"date-time":"2023-07-21T09:09:28Z","timestamp":1689930568000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922501555"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,30]]},"references-count":5,"journal-issue":{"issue":"07","published-print":{"date-parts":[[2023,10]]}},"alternative-id":["10.1142\/S1793830922501555"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922501555","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,9,30]]},"article-number":"2250155"}}