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

Department of Computer Science

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

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. © 2009 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	1841-1845
Journal	Applied Mathematics Letters
Volume	22
Issue number	12
DOIs	https://doi.org/10.1016/j.aml.2009.07.012
Publication status	Published - Dec 2009

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

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

Research Keywords

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

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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. {\textcopyright} 2009 Elsevier Ltd. All rights reserved.",

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N2 - 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. © 2009 Elsevier Ltd. All rights reserved.

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. © 2009 Elsevier Ltd. All rights reserved.

KW - Connectivity index

KW - Extremal graph

KW - Hexagonal chain

KW - Recursive formula

KW - Third-order Randić index

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DO - 10.1016/j.aml.2009.07.012

M3 - RGC 21 - Publication in refereed journal

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SP - 1841

EP - 1845

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 12

ER -

The hexagonal chains with the extremal third-order Randić index

Abstract

Bibliographical note

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Research Keywords

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