{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T02:49:05Z","timestamp":1767840545390,"version":"3.49.0"},"reference-count":40,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T00:00:00Z","timestamp":1631059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2021R1F1A1050"],"award-info":[{"award-number":["2021R1F1A1050"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The commuting graph of a finite non-abelian group G with center Z(G), denoted by \u0393c(G), is a simple undirected graph whose vertex set is G\u2216Z(G), and two distinct vertices x and y are adjacent if and only if xy=yx. Alwardi et al. (Bulletin, 2011, 36, 49-59) defined the common neighborhood matrix CN(G) and the common neighborhood energy Ecn(G) of a simple graph G. A graph G is called CN-hyperenergetic if Ecn(G)&gt;Ecn(Kn), where n=|V(G)| and Kn denotes the complete graph on n vertices. Two graphs G and H with equal number of vertices are called CN-equienergetic if Ecn(G)=Ecn(H). In this paper we compute the common neighborhood energy of \u0393c(G) for several classes of finite non-abelian groups, including the class of groups such that the central quotient is isomorphic to group of symmetries of a regular polygon, and conclude that these graphs are not CN-hyperenergetic. We shall also obtain some pairs of finite non-abelian groups such that their commuting graphs are CN-equienergetic.<\/jats:p>","DOI":"10.3390\/sym13091651","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T02:41:07Z","timestamp":1631068867000},"page":"1651","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Common Neighborhood Energy of Commuting Graphs of Finite Groups"],"prefix":"10.3390","volume":"13","author":[{"given":"Rajat Kanti","family":"Nath","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Tezpur University, Tezpur 784028, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Walaa Nabil Taha","family":"Fasfous","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tezpur University, Tezpur 784028, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2576-160X","authenticated-orcid":false,"given":"Kinkar Chandra","family":"Das","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2817-3400","authenticated-orcid":false,"given":"Yilun","family":"Shang","sequence":"additional","affiliation":[{"name":"Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,8]]},"reference":[{"key":"ref_1","first-page":"49","article-title":"On the common-neighborhood energy of a graph","volume":"36","author":"Alwardi","year":"2011","journal-title":"Bulletin"},{"key":"ref_2","first-page":"1","article-title":"The common neighborhood graph and its energy","volume":"7","author":"Alwardi","year":"2012","journal-title":"Iran. 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