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  "aliases": [
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  "body": "\n## Summary\n\nIn graph theory, the **graph bandwidth problem** may be visualized as placing the vertices of a given [[graph|00C0BR7D7H]] at distinct integer positions along the number line so that the length of the longest edge is minimized. Such placement is called **linear graph arrangement**, **linear graph layout** or **linear graph placement**. It may be formalized as labeling the $n$ vertices $v_i$ of a graph $G$ with distinct [[integers|0C4JS9RF5M]] $f(v_i)$ so that the quantity $\\max\\{\\,| f(v_i) - f(v_j)| : v_iv_j \\in E \\,\\}$ is minimized, where $E$ is the edge set of $G$.\n",
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