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Bandwidth of the composition of two graphs

2003
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Discrete Mathematics
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The bandwidth B(G) of a graph G is the minimum of the quantity max{|f(x) − f(y)| : xy ∈ E(G)} taken over all proper numberings f of G. The composition of two graphs G and H , written as G[H ], is the graph with vertex set V (G) × V (H ) and with (u1; v1) is adjacent to (u2; v2) if either u1 is adjacent to u2 in G or u1 = u2 and v1 is adjacent to v2 in H . In this paper, we investigate the bandwidth of the composition of two graphs. Let G be a connected graph. We denote the diameter of G by

doi:10.1016/s0012-365x(03)00131-6
fatcat:yeqeozyw6bbgfp7dw2b6kqimmq