A graph G is a pseudo-core if every endomorphism of G is either an automorphism or a colouring. Let F q be the finite field with q elements and let Alt ( m , q ) ( m 4 ) be the alternating forms graph on the vector space F q m . We prove that Alt ( m , q ) is a pseudo-core. Moreover, if m is odd, then Alt ( m , q ) is a core. If both m and q are even, then Alt ( m , q ) is not a core. A graph G is a pseudo-core if every endomorphism of G is either an automorphism or a colouring. Let F q be the finite field with q elements and let Alt ( m , q ) ( m 4 ) be the alternating forms graph on the vect...
