On bandwidth for the tensor product of paths and cycles Original Research Article

The tensor product of graphs G1 and G2 is defined to be G = (V, E) where V = V(G1) × V(G2) and edge ((x1, y1), (x2, y2)) ϵ E whenever (x1, x2) ϵ E(G1) and (y1, y2) ϵ E(G2). We use G1(Tp)G2 to denote G. This paper establishes the bandwidth of the tensor product of a path with a path, a cycle with a path, and a cycle with a cycle. Optimal numberings to achieve each of these bandwidths are provided.