Bounds for the bandwidth of a graph have been considered by (Harper 1964), and the bandwidth of the -cube
was determined by Harper (Harper 1966, Wang and Wu 2007, Harper 2010).

Special cases are summarized in the following table.

Böttcher, J.; Preussmann, K. P.; Taraz, A.; and Würfl, A. "Bandwidth, Expansion, Treewidth, Separators and Universality
for Bounded-Degree Graphs." Eur. J. Combin.31, 1217-1227, 2010.Chinn,
P. Z.; Chvátalová, J.; Dewdney, A. K.; and Gibbs, N. E.
"The Bandwidth Problem for Graphs and Matrices--A Survey." J. Graph
Th.6, 223-254, 1982.Chvátalová, J. "Optimal
Labelling of a Product of Two Paths." Disc. Math.11, 249-253,
1975.Harper, L. H. "Optimal Assignments of Numbers to Vertices."
J. Soc. Indust. Appl. Math.12, 131-135, 1964.Harper,
L. H. "Optimal Numberings and Isoperimetric Problems on Graphs." J.
Combin. Th.1, 385-393, 1966.Harper, L. H. Global
Methods for Combinatorial Isoperimetric Problems. Cambridge, England: Cambridge
University Press, 2010.Miller, Z. "A Linear Algorithm for Topological
Bandwidth with Degree-Three Trees." SIAM J. Comput.17, 1018-1035,
1988.Wang, X. and Wu, X. "Recursive Structure and Bandwidth of
Hales-Numbered Hypercube." 27 Aug 2007. http://arxiv.org/abs/0708.3628.West,
D. B. Introduction
to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 390,
2000.