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In this note we give a numerical expression for the bandwidth $bw(P_{n}^{d})$of the $d$-product of a path with $n$ edges, $P_{n}^{d}$. We prove that thisbandwidth is given by the sum of certain multinomial coefficients. We also showthat $bw(P_{n}^{d})$ is bounded above and below by the largest coefficient inthe expansion of $(1+x+...+x^{n})^{k}$, with $k\in{d,d+1}$. Moreover, wecompare the asymptotic behavior of $bw(P_{n}^{d})$ with the bandwidth of thelabeling obtained by ordering the vertices of $P_{n}^{d}$ in lexicographicorder.

Bandwidth of the product of paths of the same length