A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or a colouring. A graph G is a core if every endomorphism of G is an automorphism. Let F-q be the finite field with q elements where q is a power of an odd prime number. The quadratic forms graph, denoted by Quad(n, q) where n >= 2, has all quadratic forms on F-q(n) as vertices and two vertices f and g are adjacent whenever rk(f - g) = 1 or 2. We prove that every Quad(n, q) is a pseudo-core. Further, when n is even, Quad(n, q) is a core. When n is odd, Quad(n, q) is not a core. On the other hand, we complete...
