Group for Research in Decision Analysis

# The geometric-arithmetic index and the chromatic number of connected graphs

## Mustapha Aouchiche and Pierre Hansen

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 $$\omega$$.

, 10 pages