{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,20]],"date-time":"2026-07-20T11:52:57Z","timestamp":1784548377849,"version":"3.55.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $G$ be a group\u200e. \u200eThe power graph\u00a0of $G$ is a graph with the vertex\u200e \u200eset $G$\u200e, \u200ehaving an edge between two elements whenever one is a power of the other\u200e. \u200eWe characterize nilpotent groups whose power graphs have finite independence number\u200e. \u200eFor a bounded exponent group\u200e, \u200ewe prove its power graph is a perfect graph and we determine\u200e \u200eits clique\/chromatic number\u200e. \u200eFurthermore\u200e, \u200eit is proved that for every group $G$\u200e, \u200ethe clique number of the power graph of $G$ is at most countably infinite\u200e. \u200eWe also measure how close the power graph is to the commuting graph\u00a0by introducing a new graph which lies in between\u200e. \u200eWe call this new graph as the enhanced power graph\u200e. \u200eFor an arbitrary pair of these three graphs we characterize finite groups for which this pair of graphs are equal\u200e.<\/jats:p>","DOI":"10.37236\/6497","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:51:02Z","timestamp":1578653462000},"source":"Crossref","is-referenced-by-count":70,"title":["On the Structure of the Power Graph and the Enhanced Power Graph of a Group"],"prefix":"10.37236","volume":"24","author":[{"given":"Ghodratollah","family":"Aalipour","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Saieed","family":"Akbari","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter J.","family":"Cameron","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Reza","family":"Nikandish","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Farzad","family":"Shaveisi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2017,7,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p16\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:50:59Z","timestamp":1579218659000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,28]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6497","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,28]]},"article-number":"P3.16"}}