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  "body": "\n## Summary\n\nIn chemical graph theory, the **Padmakar–Ivan (PI) index** is a topological index of a molecule, used in biochemistry. The Padmakar–Ivan index is a generalization introduced by Padmakar V. Khadikar and Iván Gutman of the concept of the Wiener index, introduced by Harry Wiener. The Padmakar–Ivan index of a graph *G* is the sum over all edges *uv* of *G* of number of edges which are not equidistant from *u* and *v*. Let *G* be a graph and *e* = *uv* an edge of *G*. Here $n_{eu}(e\\mid G)$ denotes the number of edges lying closer to the vertex *u* than the vertex *v*, and $n_{ev}(e\\mid G)$ is the number of edges lying closer to the vertex *v* than the vertex *u*. The Padmakar–Ivan index of a graph *G* is defined as\n",
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