The hexagonal chains with the extremal third-order Randić index

Jie Zhang; Hanyuan Deng

doi:10.1016/j.aml.2009.07.012

The hexagonal chains with the extremal third-order Randić index

Jie Zhang, Hanyuan Deng

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

5 Citations (SciVal)

Abstract

The third-order Randić index of a graph G is defined as R₃ (G) = ∑_{u1 u2 u3 u4} frac(1, sqrt(d (u₁) d (u₂) d (u₃) d (u₄))), where the summation is taken over all possible paths of length three of G. A recursive formula for computing the third-order Randić index of a hexagonal chain is given in this paper, and the hexagonal chains with the extremal third-order Randić index are characterized.

Original language	English
Pages (from-to)	1841-1845
Number of pages	5
Journal	Applied Mathematics Letters
Volume	22
Issue number	12
Early online date	27 Jul 2009
DOIs	https://doi.org/10.1016/j.aml.2009.07.012
Publication status	Published - 31 Dec 2009

Funding

Project supported by Hunan Provincial Natural Science Foundation of China (09JJ6009).

Keywords

Connectivity index
Extremal graph
Hexagonal chain
Recursive formula
Third-order Randić index

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2009.07.012

Cite this

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title = "The hexagonal chains with the extremal third-order Randi{\'c} index",

abstract = "The third-order Randi{\'c} index of a graph G is defined as R3 (G) = ∑u1 u2 u3 u4 frac(1, sqrt(d (u1) d (u2) d (u3) d (u4))), where the summation is taken over all possible paths of length three of G. A recursive formula for computing the third-order Randi{\'c} index of a hexagonal chain is given in this paper, and the hexagonal chains with the extremal third-order Randi{\'c} index are characterized.",

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author = "Jie Zhang and Hanyuan Deng",

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AU - Deng, Hanyuan

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AB - The third-order Randić index of a graph G is defined as R3 (G) = ∑u1 u2 u3 u4 frac(1, sqrt(d (u1) d (u2) d (u3) d (u4))), where the summation is taken over all possible paths of length three of G. A recursive formula for computing the third-order Randić index of a hexagonal chain is given in this paper, and the hexagonal chains with the extremal third-order Randić index are characterized.

KW - Connectivity index

KW - Extremal graph

KW - Hexagonal chain

KW - Recursive formula

KW - Third-order Randić index

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 12

ER -

The hexagonal chains with the extremal third-order Randić index

Abstract

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Keywords

ASJC Scopus subject areas

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