The geometric–arithmetic index and the chromatic number of connected graphs

Mustapha Aouchiche; Pierre Hansen

doi:10.1016/j.dam.2017.08.003

The geometric–arithmetic index and the chromatic number of connected graphs

Mustapha Aouchiche, Pierre Hansen

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

7 Citations (Scopus)

Abstract

In the present paper, we compare the geometric–arithmetic index GA and the chromatic number χ of a connected graph with given order. We prove, among other results, an upper bound on the ratio GA∕χ. We also prove lower bounds on the chromatic number in terms of geometric–arithmetic index and number of vertices of a connected graph. The results obtained for the chromatic number χ are extended to the clique number ω.

Original language	English
Pages (from-to)	207-212
Number of pages	6
Journal	Discrete Applied Mathematics
Volume	232
DOIs	https://doi.org/10.1016/j.dam.2017.08.003
Publication status	Published - Dec 11 2017
Externally published	Yes

Keywords

Chromatic number
Clique number
Conjecture
Geometric–arithmetic index
Graph

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2017.08.003

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abstract = "In the present paper, we compare the geometric–arithmetic index GA and the chromatic number χ of a connected graph with given order. We prove, among other results, an upper bound on the ratio GA∕χ. We also prove lower bounds on the chromatic number in terms of geometric–arithmetic index and number of vertices of a connected graph. The results obtained for the chromatic number χ are extended to the clique number ω.",

keywords = "Chromatic number, Clique number, Conjecture, Geometric–arithmetic index, Graph",

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AU - Aouchiche, Mustapha

AU - Hansen, Pierre

PY - 2017/12/11

Y1 - 2017/12/11

N2 - In the present paper, we compare the geometric–arithmetic index GA and the chromatic number χ of a connected graph with given order. We prove, among other results, an upper bound on the ratio GA∕χ. We also prove lower bounds on the chromatic number in terms of geometric–arithmetic index and number of vertices of a connected graph. The results obtained for the chromatic number χ are extended to the clique number ω.

AB - In the present paper, we compare the geometric–arithmetic index GA and the chromatic number χ of a connected graph with given order. We prove, among other results, an upper bound on the ratio GA∕χ. We also prove lower bounds on the chromatic number in terms of geometric–arithmetic index and number of vertices of a connected graph. The results obtained for the chromatic number χ are extended to the clique number ω.

KW - Chromatic number

KW - Clique number

KW - Conjecture

KW - Geometric–arithmetic index

KW - Graph

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

The geometric–arithmetic index and the chromatic number of connected graphs

Abstract

Keywords

ASJC Scopus subject areas

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