The Factorization of Locally Finite Graphs

Source abstract

1. Introduction. A graph G consists of a set V(G) of objects called nodes and a set M (G) of objects called links , V(G) and M (G) having no members in common. With each link A there is associated just two nodes said to be the ends of A, or to be incident with A, or to be joined by A. The sets V(G) and M(G) may be finite or infinite. There may be nodes with which no link is incident. Such nodes are said to be isolated .