{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:25Z","timestamp":1753893865712,"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>Let $k\\ge 3$ be an integer, $q$ be a prime power, and $\\mathbb{F}_q$ denote the field of $q$ elements. Let $f_i, g_i\\in\\mathbb{F}_q[X]$, $3\\le i\\le k$, such that $g_i(-X) = -\\, g_i(X)$. We define a graph $S(k,q) = S(k,q;f_3,g_3,\\cdots,f_k,g_k)$ as a graph with the vertex set $\\mathbb{F}_q^k$ and edges defined as follows: vertices $a = (a_1,a_2,\\ldots,a_k)$ and $b = (b_1,b_2,\\ldots,b_k)$ are adjacent if $a_1\\ne b_1$ and the following $k-2$ relations on their components hold:$$b_i-a_i = g_i(b_1-a_1)f_i\\Bigl(\\frac{b_2-a_2}{b_1-a_1}\\Bigr)\\;,\\quad 3\\le i\\le k.$$ We show that the graphs $S(k,q)$ generalize several recently studied examples of regular expanders and can provide many new such examples.<\/jats:p>","DOI":"10.37236\/7950","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T14:45:39Z","timestamp":1578667539000},"source":"Crossref","is-referenced-by-count":0,"title":["Spectral and Combinatorial Properties of Some Algebraically Defined Graphs"],"prefix":"10.37236","volume":"25","author":[{"given":"Sebastian M.","family":"Cioab\u0103","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Felix","family":"Lazebnik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuying","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2018,12,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p60\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p60\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:19:25Z","timestamp":1579234765000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p60"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,21]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7950","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,12,21]]},"article-number":"P4.60"}}