The bandwidth of a connected graph G is the minimum matrix bandwidth among all possible adjacency matrices of graphs isomorphic to G. Equivalently, it is the minimum graph dilation of a numbering of a graph. Bandwidth is variously denoted b w(G), B(G), or φ(G). The bandwidth of the singleton graph is not defined, but the conventions b w(K_1) = 0 or b w(K_1) = 1 are sometimes adopted. The bandwidth of a disconnected graph is the maximum of the bandwidths of its connected components.
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