Common factors of integers: A graphic view (Q1101136)

From author's abstract: ``The common factor graph of a set of integers has the integers as vertices, two vertices being adjacent just if they have a proper common factor. A characterization of common factor graphs is given. The common factor graph of P, the set of integers \(\geq 2\), is a diameter 2 graph in which every included subgraph is a common factor graph, and every common factor graph is isomorphic to an induced subgraph of the common factor graph of P. We discuss the problem of finding the length of the smallest initial segment of P which contains a given finite graph as an induced subgraph. Connected common factor graphs of runs of consecutive integers are considered in detail.''