A graph G is a core if every endomorphism of G is an automorphism. Let J(q) (n, m) be the Grassmann graph with parameters q, m, n. We prove that many Grassmann graphs are cores, and both J(2)(2k, 2) and J(q) (2k, 2) are not cores. We also obtain the independence number of Jq (n, 2). In further to study cores and coding theory, it is important to estimate the upper bound of the independence number of J(q) (n, m). Using a vertex-transitive subgraph of J(q) (n, m), we obtain upper bounds on the independence number of J(q) (n, m), which are also an improvement of bounds for the...
