{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:55:01Z","timestamp":1780386901540,"version":"3.54.1"},"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>In this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of $(q+1,8)$-cages, for $q$ a prime power. We remove vertices from such cages and add matchings among the vertices of minimum degree to achieve regularity in the new graphs. We obtain $(q+1)$-regular graphs of girth 7 and order $2q^3+q^2+2q$ for each even prime power $q \\ge 4$, and of order $2q^3+2q^2-q+1$ for each odd prime power $q\\ge 5$.\u00a0A corrigendum was added to this paper on 21 June 2016.<\/jats:p>","DOI":"10.37236\/4205","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:35:41Z","timestamp":1578699341000},"source":"Crossref","is-referenced-by-count":1,"title":["Small Regular Graphs of Girth 7"],"prefix":"10.37236","volume":"22","author":[{"given":"M.","family":"Abreu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G.","family":"Araujo-Pardo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C.","family":"Balbuena","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Labbate","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Salas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2015,7,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i3p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:14:42Z","timestamp":1579256082000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i3p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,1]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2015,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/4205","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,7,1]]},"article-number":"P3.5"}}