An algorithm for the number of path homomorphisms

A homomorphism of a graph G 1 = ( V 1 , E 1 ) to a graph G 2 = ( V 2 , E 2 ) is a mapping from the vertex set V 1 of G 1 to the vertex set V 2 of G 2 which preserves edges. In this paper we provide an algorithm to determine the number of homomorphisms from an arbitrary finite undirected path to another arbitrary finite undirected path.