The endomorphisms of Grassmann graphs

Li-Ping Huang, Benjian Lv, Kaishun Wang

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 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.


Keywords


Grassmann graph, core, pseudo-core, endomorphism, maximal clique

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DOI: https://doi.org/10.26493/1855-3974.780.362

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications