---
tag: 2CJG7QJ4HA
kind: concept
name: Padmakar–Ivan index
sources:
  - wikipedia: en:56103252@r1371423699
    locator: Padmakar–Ivan index
    note: adopted
    mention: wikipedia://en/56103252
    sections: [Summary]
same_as:
  wikidata: Q56291683
  wikipedia: Padmakar–Ivan index
inventory: [N3JB5KAWDV]
---

## Summary

In 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