On the geometric–arithmetic index of a graph.

Abstract Very recently, Aouchiche and Hansen gave an upper bound on the ratio of G A ∕ χ of the geometric–arithmetic index G A (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 G A (G − e) < G A (G). [ABSTRACT FROM AUTHOR]