In the present paper, we compare the geometric-arithmetic index \(GA\) and the chromatic number \(\chi\) of a connected graph with given order. We prove, among other results, an upper bound on the ratio \(GA/\chi\). 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 \(\chi\) are extended to the clique number \(\omega\).