Abstract
We give a general Harper-type lower bound for the bandwidth of a graph which is a common generalization of several known results. As applications we get a lower bound for the bandwidth of the composition of two graphs. By using this we determine the bandwidths of some composition graphs such as ( P r × P s )[ H], ( P r × C s )[ H] (2 r ≠ s), ( C r × C s )[ H] (6 ⩽ 2 r ⩽ s), etc., for any graph H. Interestingly, the bandwidths of these graphs have nothing to do with the structure of H in general.
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