## Abstract

The Padmakar-Ivan (PI) index is a graph invariant defined as the summation of the sums of n_{eu} (e|G) and n _{ev}(e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = Σ _{e∈E(G)}[n_{eu}(e|G) + n_{ev}(e|G)], where n _{eu}(e|G) is the number of edges of G lying closer to u than to v and n_{ev}(e|G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of phenylenes is given, and a simple relation is established between the PI index of a phenylene and of the corresponding hexagonal squeeze.

Original language | English |
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Pages (from-to) | 63-69 |

Number of pages | 7 |

Journal | Journal of Mathematical Chemistry |

Volume | 41 |

Issue number | 1 |

DOIs | |

Publication status | Published - 31 Jan 2007 |

### Funding

Project 10471037 supported by the National Natural Science Foundation of China and Project 04B047 Supported by Scientific Research Fund of Hunan Provincial Education Department.

Funders | Funder number |
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Scientific Research Foundation of Hunan Provincial Education Department | |

National Natural Science Foundation of China | 04B047 |

## Keywords

- Hexagonal squeeze
- Phenylene
- PI index

## ASJC Scopus subject areas

- General Chemistry
- Applied Mathematics