{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T02:34:43Z","timestamp":1768271683160,"version":"3.49.0"},"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>Let $2 \\le r &lt; m$ and $g$ be positive integers. An $(\\{r,m\\};g)$-graph (or biregular graph) is a graph with degree set $\\{r,m\\}$ and girth $g$, and an $(\\{r,m\\};g)$-cage (or biregular cage) is an $(\\{r,m\\};g)$-graph of minimum order $n(\\{r,m\\};g)$. If $m=r+1$, an $(\\{r,m\\};g)$-cage is said to be a\u00a0semiregular cage.In this paper we generalize the reduction and graph amalgam operations from [M. Abreu,\u00a0 G. Araujo-Pardo, C. Balbuena, D. Labbate. Families of Small Regular Graphs of Girth $5$. Discrete Math.\u00a0312 (2012) 2832--2842] on the incidence graphs of an affine and a biaffine plane obtaining two new infinite families of biregular cages and two new semiregular cages. The constructed new families are $(\\{r,2r-3\\};5)$-cages for all $r=q+1$ with $q$ a prime power, and $(\\{r,2r-5\\};5)$-cages for all $r=q+1$ with $q$ a prime. The new semiregular cages are constructed for $r=5$ and $6$ with $31$ and $43$ vertices respectively.<\/jats:p>","DOI":"10.37236\/2594","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:56:24Z","timestamp":1578711384000},"source":"Crossref","is-referenced-by-count":4,"title":["Biregular Cages  of Girth Five"],"prefix":"10.37236","volume":"20","author":[{"given":"Mari\u00e9n","family":"Abreu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gabriela","family":"Araujo-Pardo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Camino","family":"Balbuena","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Domenico","family":"Labbate","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gloria","family":"L\u00f3pez-Ch\u00e1vez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2013,3,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p71\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p71\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:23:23Z","timestamp":1579260203000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p71"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,31]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2594","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,3,31]]},"article-number":"P71"}}