In graph theory, the graph bandwidth problem is to label the n vertices vi of a graph G with distinct integers so that the quantity is minimized (E is the edge set of G).[1]
The problem may be visualized as placing the vertices of a graph at distinct integer points along the x-axis so that the length of the longest edge is minimized. Such placement is called linear graph arrangement, linear graph layout or linear graph placement.[2]
The weighted graph bandwidth problem is a generalization wherein the edges are assigned weights wij and the cost function to be minimized is .
In terms of matrices, the (unweighted) graph bandwidth is the minimal bandwidth of a symmetric matrix which is an adjacency matrix of the graph.
The bandwidth may also be defined as one less than the maximum clique size in a proper interval supergraph of the given graph, chosen to minimize its clique size (Kaplan & Shamir 1996).
^(Chinn et al. 1982)
^Cite error: The named reference feige was invoked but never defined (see the help page).
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