{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:36Z","timestamp":1753893816708,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a graph $G$, its $r$th power is constructed by placing an edge between two vertices if they are within distance $r$ of each other. In this note we study the amount of edges added to a graph by taking its $r$th power.  In particular we obtain that, for $r\\geq 3$, either the $r$th power is complete or \"many\" new edges are added.  In this direction, Hegarty showed that there is a constant $\\epsilon &gt; 0$ such $e(G^3)\\geq (1+\\epsilon)e(G)$.  We extend this result in two directions.  We give an alternative proof of Hegarty's result with an improved constant of $\\epsilon = \\frac{1}{6}$.  We also show that for general $r$, $e(G^{r}) \\geq \\left( \\left\\lceil \\frac{r}{3} \\right\\rceil -1 \\right)e(G).$<\/jats:p>","DOI":"10.37236\/575","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:48:37Z","timestamp":1578714517000},"source":"Crossref","is-referenced-by-count":1,"title":["Growth of Graph Powers"],"prefix":"10.37236","volume":"18","author":[{"given":"A.","family":"Pokrovskiy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,4,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p88\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p88\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:13:16Z","timestamp":1579302796000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p88"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/575","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,4,14]]},"article-number":"P88"}}