The PI index of phenylenes

Hanyuan Deng; Shubo Chen; Jie Zhang

doi:10.1007/s10910-006-9198-2

The PI index of phenylenes

Hanyuan Deng, Shubo Chen, Jie Zhang

Research output: Contribution to journal › Article › peer-review

40 Citations (SciVal)

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
Pages (from-to)	63-69
Number of pages	7
Journal	Journal of Mathematical Chemistry
Volume	41
Issue number	1
DOIs	https://doi.org/10.1007/s10910-006-9198-2
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
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

Access to Document

10.1007/s10910-006-9198-2

Cite this

@article{35be0cdd7b624a6a8e688fa2762e8cc9,

title = "The PI index of phenylenes",

abstract = "The Padmakar-Ivan (PI) index is a graph invariant defined as the summation of the sums of neu (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)[neu(e|G) + nev(e|G)], where n eu(e|G) is the number of edges of G lying closer to u than to v and nev(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.",

keywords = "Hexagonal squeeze, Phenylene, PI index",

author = "Hanyuan Deng and Shubo Chen and Jie Zhang",

year = "2007",

month = jan,

day = "31",

doi = "10.1007/s10910-006-9198-2",

language = "English",

volume = "41",

pages = "63--69",

journal = "Journal of Mathematical Chemistry",

issn = "0259-9791",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - The PI index of phenylenes

AU - Deng, Hanyuan

AU - Chen, Shubo

AU - Zhang, Jie

PY - 2007/1/31

Y1 - 2007/1/31

N2 - The Padmakar-Ivan (PI) index is a graph invariant defined as the summation of the sums of neu (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)[neu(e|G) + nev(e|G)], where n eu(e|G) is the number of edges of G lying closer to u than to v and nev(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.

AB - The Padmakar-Ivan (PI) index is a graph invariant defined as the summation of the sums of neu (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)[neu(e|G) + nev(e|G)], where n eu(e|G) is the number of edges of G lying closer to u than to v and nev(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.

KW - Hexagonal squeeze

KW - Phenylene

KW - PI index

UR - https://www.scopus.com/pages/publications/33846408031

U2 - 10.1007/s10910-006-9198-2

DO - 10.1007/s10910-006-9198-2

M3 - Article

AN - SCOPUS:33846408031

SN - 0259-9791

VL - 41

SP - 63

EP - 69

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 1

ER -

The PI index of phenylenes

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this