Bandwidth of the product of paths of the same length

Abstract. In this note we give a numerical expression for the bandwidth bw(P d n) of the dproduct of a path with n edges, P d n . We prove that this bandwidth is given by the sum of certain multinomial coefficients. We also show that bw(P d n) is bounded above and below by the largest coefficient in the expansion of (1 + x + · · ·+ x), with k ∈ {d, d + 1}. Moreover, we compare the asymptotic behavior of bw(P d n) with the bandwidth of the labeling obtained by ordering the vertices of P d n in lexicographic order.