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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 graphs $S(k,q)$ gene","authors_text":"Felix Lazebnik, Sebastian M. 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