An algorithm for the number of path homomorphisms

A homomorphism of a graph G1=(V1,E1)G1=(V1,E1) to a graph G2=(V2,E2)G2=(V2,E2) is a mapping from the vertex set V1V1 of G1G1 to the vertex set V2V2 of G2G2 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.