Number of Fixed Points of <i>k</i>-Almost and <i>k</i>-Nearly Quadratic Digraphs Associated with <i>x</i><sup>2</sup> ≡ <i>y</i> ± <i>k</i>(mod <i>p</i>) where <i&

Let n and k be positive integers. We define a quadratic digraph G+(-)(2, k, n) over the residue classes of n where the vertex set of G+(-)(2, k, n) is the set of complete residue class of all integers when divided by n, {0, 1, 2,..., n-1} and (u, v) is a directed edge of G+(-)(2, k, n) from a vertex u to a vertex v if u2 ≡ v + (-)k (mod n). G+(-)(2, k, n) is called the k-almost (k-nearly) quadratic digraph. When k=1, G+(-)(2, 1, n) is also called the almost (nearly) quadratic digraph. Let p be an odd prime. We consider the fixed points of a quadratic digraph G+(-)(2, k, p). Depending on the remainder when p is divided by certain prime numbers, we obtain the number of fixed points of k-almost and k-nearly quadratic digraph where k ∈ {1, 2, 3}.