Abstract
Very recently, Aouchiche and Hansen gave an upper bound on the ratio of GA∕χ of the geometric–arithmetic index GA(G) and the chromatic number χ(G) of a graph. Furthermore, they proposed several conjectures on the relation between geometric–arithmetic index and chromatic number, and clique number. In this note, we disprove four of those conjectures. In addition, we present a sufficient condition for an edge e∈E(G) with GA(G−e)<GA(G).
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