2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69035In the paper we state and prove theorem describing the upper bound on number of the graphs that have fixed number of vertices |V| and can be colored with the fixed number of n colors. The bound relates both numbers using power of 2, while the exponent is the difference between |V| and n. We also state three conjectures on the number of graphs that have fixed number of vertices |V| and chromatic number n.7 pages, submitted for journal publicationCombinatorics05C15 ; 05C30text