{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:11Z","timestamp":1753893851255,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a field $\\mathbb{F}$ and functions $f,g,h,j\\colon\\mathbb{F}\\to \\mathbb{F}$, we define $\\Gamma_\\mathbb{F}(f(X)h(Y),g(X) j(Y))$ to be a bipartite graph where each partite set is a copy of $\\mathbb{F}^3$, and a vertex $(a,a_2,a_3)$ in the first partite set is adjacent to a vertex $[x,x_2,x_3]$ in the second partite set if and only if \\[a_2+x_2=f(a)h(x) \\quad \\text{and} \\quad a_3+x_3=g(a)j(x).\\] In this paper, we completely classify all such graphs by girth in the case $h=j$ (subject to some mild restrictions on $h$). We also present a partial classification when $h\\neq j$ and provide some applications.<\/jats:p>","DOI":"10.37236\/9749","type":"journal-article","created":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T18:16:55Z","timestamp":1667499415000},"source":"Crossref","is-referenced-by-count":1,"title":["On the Girth of Three-Dimensional Algebraically Defined Graphs with Multiplicatively Separable Functions"],"prefix":"10.37236","volume":"29","author":[{"given":"Alex M.","family":"Kodess","sequence":"first","affiliation":[]},{"given":"Brian G.","family":"Kronenthal","sequence":"additional","affiliation":[]},{"given":"Tony W.H.","family":"Wong","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2022,11,4]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i4p21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i4p21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T18:16:56Z","timestamp":1667499416000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i4p21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,4]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,10,6]]}},"URL":"https:\/\/doi.org\/10.37236\/9749","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2022,11,4]]},"article-number":"P4.21"}}