On polynomial digraphs

Let $\Phi(x,y)$ be a bivariate polynomial with complex coefficients. The zeroes of $\Phi(x,y)$ are given a combinatorial structure by considering them as arcs of a directed graph $G(\Phi)$. This paper studies some relationship between the polynomial $\Phi(x,y)$ and the structure of $G(\Phi)$.Comment: 13 pages, 6 figures, See also http://www-ma2.upc.edu/~montes

Xk-Digraphs

AbstractLet G be a directed graph on n vertices (single loops allowed) such that there are λ directed paths of length k from P to Q for any distinct pair of vertices (P, Q). We prove that if n > 2 and k > 2, G is regular. The regular case is also discussed