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Graphs and Combinatorics | Vol., Issue. | | Pages 1–13
Endomorphisms of Twisted Grassmann Graphs
A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or a colouring. An interesting problem in graph theory is to distinguish whether a graph is a core. The twisted Grassmann graphs, constructed by van Dam and Koolen in (Invent Math 162:189–193, 2005), are the first known family of non-vertex-transitive distance-regular graphs with unbounded diameter. In this paper, we show that every twisted Grassmann graph is a pseudo-core.
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Endomorphisms of Twisted Grassmann Graphs
A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or a colouring. An interesting problem in graph theory is to distinguish whether a graph is a core. The twisted Grassmann graphs, constructed by van Dam and Koolen in (Invent Math 162:189–193, 2005), are the first known family of non-vertex-transitive distance-regular graphs with unbounded diameter. In this paper, we show that every twisted Grassmann graph is a pseudo-core.
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