Abstract
A graph G is a core if every endomorphism of G is an automorphism. A graph is called a pseudo-core if every its endomorphism is either an automorphism or a colouring. Suppose that J q ( n , m ) is a Grassmann graph over a finite field with q elements. We show that every Grassmann graph is a pseudo-core. Moreover, J 2 (4, 2) is not a core and J q (2 k + 1, 2) ( k ≥ 2 ) is a core.
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