A graph is called a pseudo-core if every endomorphism is either an
automorphism or a colouring. In this paper, we show that every Grassmann graph
Jqβ(n,m) is a pseudo-core. Moreover, the Grassmann graph Jqβ(n,m) is a core
whenever m and nβm+1 are not relatively prime, and Jqβ(2pkβ2,pkβ1) is a
core whenever p,kβ₯2.Comment: 8 page