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By combining a graph structure with a fuzzy graph, a fuzzy graph structure was introduced that increased the decision-making power of complex problems based on uncertainties. The previous definitions restrictions in fuzzy graphs have made us present new definitions in the fuzzy graph structure. The domination of fuzzy graphs has many applications in other sciences including computer science, intelligent systems, psychology, and medical sciences. Hence, in this paper, first we study the dominating set in a fuzzy graph structure from the perspective of the domination number of its fuzzy relationships. Likewise, we determine the domination in terms of neighborhood, degree, and capacity of vertices with some examples. Finally, applications of domination are introduced in fuzzy graph structure.<\/jats:p>","DOI":"10.3233\/jifs-211923","type":"journal-article","created":{"date-parts":[[2021,11,9]],"date-time":"2021-11-09T12:57:02Z","timestamp":1636462622000},"page":"3705-3718","source":"Crossref","is-referenced-by-count":2,"title":["New concepts of domination in fuzzy graph structures with application"],"prefix":"10.1177","volume":"42","author":[{"given":"A.A.","family":"Talebi","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Mazandaran, Babolsar, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Muhiuddin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.H.","family":"Sadati","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Mazandaran, Babolsar, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hossein","family":"Rashmanlou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Mazandaran, Babolsar, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"2","key":"10.3233\/JIFS-211923_ref1","first-page":"219","article-title":"Intuitionistic fuzzy graph structures,Kragujevac","volume":"41","author":"Akram","year":"2017","journal-title":"Journal of Mathematics"},{"key":"10.3233\/JIFS-211923_ref2","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1186\/s40064-016-3066-8","article-title":"On m-polar fuzzy graphstructures","volume":"5","author":"Akram","year":"2016","journal-title":"Springer Plus"},{"key":"10.3233\/JIFS-211923_ref3","first-page":"277","article-title":"Single-valued neutrosophic graph structures","volume":"17","author":"Akram","year":"2017","journal-title":"Applied Mathematics E-Notes"},{"issue":"1\u20132","key":"10.3233\/JIFS-211923_ref4","first-page":"25","article-title":"Certain fuzzy graph structures","volume":"61","author":"Akram","year":"2019","journal-title":"Journalof Applied Mathematics and Computing"},{"issue":"34","key":"10.3233\/JIFS-211923_ref5","first-page":"365","article-title":"Residue product of fuzzy graphstructures","volume":"34","author":"Akram","year":"2020","journal-title":"Journal of Multiple-Valued Logic and SoftComputing"},{"key":"10.3233\/JIFS-211923_ref6","first-page":"45","article-title":"A roster of worldcities","volume":"16","author":"Beaverstok","year":"1999","journal-title":"Cities"},{"key":"10.3233\/JIFS-211923_ref7","first-page":"297","article-title":"Some remarks on fuzzy graphs","volume":"6","author":"Bhattacharya","year":"1987","journal-title":"PatternRecognition Letter"},{"key":"10.3233\/JIFS-211923_ref8","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/S0020-0255(02)00411-5","article-title":"Strong arcs in fuzzy graphs","volume":"152","author":"Bhutani","year":"2003","journal-title":"Information Sciences"},{"key":"10.3233\/JIFS-211923_ref9","doi-asserted-by":"crossref","first-page":"1933","DOI":"10.3233\/IFS-151671","article-title":"Domination in vague graphs and itsapplications","volume":"29","author":"Borzooei","year":"2015","journal-title":"J. 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