{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:46Z","timestamp":1753893826131,"version":"3.41.2"},"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 $\\mathrm{AD}(G_{n,d})$ be the average distance of $G_{n,d}$, a random $n$-vertex $d$-regular graph.\r\nFor $d=(\\beta+o(1))n^{\\alpha}$ with two arbitrary constants $\\alpha\\in(0,1)$ and $\\beta&gt;0$, we prove that $|\\mathrm{AD}(G_{n,d})-\\mu|&lt;\\epsilon$ holds with high probability for any constant $\\epsilon&gt;0$, where $\\mu$ is equal to $\\alpha^{-1}+\\exp(-\\beta^{1\/\\alpha})$ if $\\alpha^{-1}\\in\\mathbb{N}$ and to $\\lceil\\alpha^{-1}\\rceil$ otherwise.\r\nConsequently, we show that the diameter of the $G_{n,d}$ is equal to $\\lfloor\\alpha^{-1}\\rfloor+1$ with high probability.<\/jats:p>","DOI":"10.37236\/8705","type":"journal-article","created":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T09:41:00Z","timestamp":1600422060000},"source":"Crossref","is-referenced-by-count":1,"title":["The Average Distance and the Diameter of Dense Random Regular Graphs"],"prefix":"10.37236","volume":"27","author":[{"given":"Nobutaka","family":"Shimizu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,9,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p62\/8181","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p62\/8181","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T09:41:00Z","timestamp":1600422060000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p62"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,18]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8705","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,9,18]]},"article-number":"P3.62"}}