On bandwidth and edgesum for the composition of two graphs Original Research Article

The composition of two graphs G and H, written G[H], is the graph with vertex set V(G) × V(H) and with (u1, v1) adjacent to (u2, v2) if either u1 is adjacent to u2 in G or u1 = u2 and v1 is adjacent to v2 in H. In this paper, we investigate the bandwidth problem for the composition of two graphs and obtain the bandwidth for several classes of graphs of the forms Kn[G] and K1,n[G]. We also provide optimal numberings which solve the graph edgesum problem for Kn[Pm] and Kn[Cm].