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 Jq(n, m) is a Grassmann graph over a finite field with q elements. We show that every Grassmann graph is a pseudo-core. Moreover, J2(4, 2) is not a core and Jq(2k + 1, 2) (k ≥ 2) is a core.
@article{780,
title = {The endomorphisms of Grassmann graphs},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {12},
year = {2016},
doi = {10.26493/1855-3974.780.362},
language = {EN},
url = {http://dml.mathdoc.fr/item/780}
}
Huang, Li-Ping; Lv, Benjian; Wang, Kaishun. The endomorphisms of Grassmann graphs. ARS MATHEMATICA CONTEMPORANEA, Tome 12 (2016) . doi : 10.26493/1855-3974.780.362. http://gdmltest.u-ga.fr/item/780/