Geodesic
A formula for the number of weak endomorphisms on paths
Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 270-279.

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A weak endomorphisms of a graph is a mapping on the vertex set of the graph which preserves or contracts edges. In this paper we provide a formula to determine the cardinalities of weak endomorphism monoids of finite undirected paths.
Keywords: path, weak endomorphisms, three-dimensional square lattices. 
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Ulrich Knauer; Nirutt Pipattanajinda. A formula for the number of weak endomorphisms on paths. Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 270-279. http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a5/

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