{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:09:02Z","timestamp":1753880942807,"version":"3.41.2"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p> Let [Formula: see text] be a graph. A subset [Formula: see text] of [Formula: see text] is called a dominating set of [Formula: see text] if every vertex not in [Formula: see text] is adjacent to some vertex in [Formula: see text] The domination number\u00a0[Formula: see text] of [Formula: see text] is the minimum cardinality taken over all dominating sets of\u00a0[Formula: see text] A dominating set [Formula: see text] is called a connected dominating set if the induced subgraph [Formula: see text] is connected. The minimum cardinality taken over all connected dominating sets of [Formula: see text] is called the connected domination number of [Formula: see text] and is denoted by [Formula: see text] In this paper, we give the exact values of domination parameters for edge cycle graphs [Formula: see text] where [Formula: see text] and [Formula: see text] Also, we obtain bounds for the domination parameters of edge cycle graphs [Formula: see text] where [Formula: see text] is an arbitrary graph and [Formula: see text] and characterize the extremal graphs. Moreover, Nordhaus\u2013Gaddum-type results are presented for the domination parameters of edge cycle graphs. <\/jats:p>","DOI":"10.1142\/s1793830922501208","type":"journal-article","created":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T07:59:12Z","timestamp":1654761552000},"source":"Crossref","is-referenced-by-count":1,"title":["Domination in edge cycle graphs"],"prefix":"10.1142","volume":"15","author":[{"given":"E.","family":"Murugan","sequence":"first","affiliation":[{"name":"Department of Mathematics, C. S. I Jayaraj Annapackiam College, Nallur 627 853, Tamil Nadu, India"}]},{"given":"G. R.","family":"Sivaprakash","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Einstein College of Arts and Science, Tirunelveli 627 012, Tamil Nadu, India"}]}],"member":"219","published-online":{"date-parts":[[2022,7,29]]},"reference":[{"issue":"4","key":"S1793830922501208BIB001","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.dam.2011.12.018","volume":"161","author":"Aouchiche M.","year":"2013","journal-title":"Discrete Appl. Math."},{"key":"S1793830922501208BIB002","first-page":"233","volume":"96","author":"Riasat A.","year":"2015","journal-title":"Utilitas Math."},{"volume-title":"Theory of Graphs and Its Applications","year":"1962","author":"Berge C.","key":"S1793830922501208BIB003"},{"key":"S1793830922501208BIB004","first-page":"81","volume":"34","author":"Brigham R. C.","year":"2000","journal-title":"J. Combin. Comput. Combin. 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