On the number of congruence classes of paths
Abstract
Let Pn denote the undirected path of length n-1. The cardinality of the set of congruence classes induced by the graph homomorphisms from Pn onto Pk is determined. This settles an open problem of Michels and Knauer (Disc. Math., 309\ (2009)\ 5352-5359). Our result is based on a new proven formula of the number of homomorphisms between paths.
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