On bandwidth for the tensor product of paths and cycles (Q678881)

The tensor product of graphs \(G_1\) and \(G_2\), denoted by \(G_1(T_P)G_2\), is the graph which has vertex set \(V(G_1) \times V(G_2)\) and edges defined by: \((x_1,y_1)\) is adjacent to \((x_2,y_2)\) when \((x_1,x_2) \in E(G_1)\) and \((y_1,y_2) \in E(G_2)\). The authors obtain the bandwidth and provide an optimal numbering with this bandwidth for the following tensor products: path and path, path and cycle, cycle and cycle.