Let q be a power of 2, and let Fq be the finite field with q elements. The quadratic forms graph, denoted by Q(n,q) where n≥ 2 , has all quadratic forms on Fqn as vertices and two vertices f and g are adjacent if rk (f- g) = 1 or 2. 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. We prove that Q(n,q) is a pseudo-core and Q(2m,q) is a core. Moreover, we gave the smallest eigenvalue of Q(n,q). © 2019, Spr...
