A Remark on Dot-Compositions of Graphs

Abstract

If G and H are graphs with the property that the identification of any vertex of G with an arbitrary vertex of H results in a unique graph (up to isomorphism), then we write G.H for the thus obtained graph. This definition is in [2], p. 23. The graph G.H is called the dot-composition of G and H, the graphs G and H are called dot-components of this graph.