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In this paper, we consider non-commuting graphs associated to dihedral and semidihedral groups. We investigate their metric properties such as center, periphery, eccentric graph, closure and interior. We also perform various types of metric identifications on these graphs. Moreover, we generate metric and metric-degree polynomials of these graphs. <\/jats:p>","DOI":"10.1142\/s0129054122420229","type":"journal-article","created":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T01:31:11Z","timestamp":1662946271000},"page":"931-952","source":"Crossref","is-referenced-by-count":1,"title":["Metric Properties of Non-Commuting Graph Associated to Two Groups"],"prefix":"10.1142","volume":"33","author":[{"given":"Salman","family":"Mukhtar","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]},{"given":"Muhammad","family":"Salman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]},{"given":"Ayse Dilek","family":"Maden","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Selcuk University, Konya 42005, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6343-0620","authenticated-orcid":false,"given":"Masood","family":"Ur Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Selcuk University, Konya 42005, Turkey"},{"name":"Department of Mathematics, University College of Zhob, BUITEMS, Zhob 85200, Pakistan"}]}],"member":"219","published-online":{"date-parts":[[2022,9,10]]},"reference":[{"key":"S0129054122420229BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.02.015"},{"key":"S0129054122420229BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00435-6"},{"key":"S0129054122420229BIB003","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2015.1053488"},{"key":"S0129054122420229BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2019.2938083"},{"key":"S0129054122420229BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-011-0121-3"},{"key":"S0129054122420229BIB006","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7840"},{"key":"S0129054122420229BIB007","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2014.897188"},{"key":"S0129054122420229BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90202-5"},{"key":"S0129054122420229BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90004-3"},{"key":"S0129054122420229BIB010","doi-asserted-by":"publisher","DOI":"10.1515\/spma-2016-0012"},{"key":"S0129054122420229BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2005.09.003"},{"key":"S0129054122420229BIB012","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623714"},{"key":"S0129054122420229BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2008.11.034"},{"key":"S0129054122420229BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-008-9132-y"},{"key":"S0129054122420229BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00198-0"},{"key":"S0129054122420229BIB016","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2015.1065866"},{"key":"S0129054122420229BIB017","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2015.1110588"},{"key":"S0129054122420229BIB018","doi-asserted-by":"publisher","DOI":"10.1080\/03081087.2016.1234577"},{"key":"S0129054122420229BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/s10910-018-0877-6"},{"key":"S0129054122420229BIB020","first-page":"191","volume":"2","author":"Harary F.","year":"1976","journal-title":"Ars Combinatoria"},{"issue":"1","key":"S0129054122420229BIB021","volume":"17","author":"Hernando C.","year":"2010","journal-title":"The Electronic Journal of Combinatorics [electronic only]"},{"key":"S0129054122420229BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2012.07.025"},{"key":"S0129054122420229BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2018.05.052"},{"issue":"19","key":"S0129054122420229BIB024","first-page":"9790","volume":"218","author":"Kratica J.","year":"2012","journal-title":"Appl. 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