New upper bounds for the chromatic number of a graph

For a connected graph G of order n, the clique number ω(G), the chromatic number χ(G) and the independence number α(G) satisfy ω(G) ≤ χ(G) ≤ n − α(G) + 1. We will show that the arithmetic mean of the previous lower and upper bound provides a new upper bound for the chromatic number of a graph.