# Computation of Chromatic number

What little i know is that a discrete graph and an empty graph has chromatic number $$1$$, while a complete graph with $$n$$ vertices has a chromatic number $$n$$. I am curious to know whether there is any known formula to calculate the chromatic number of a simple graph $$G$$ just by knowing its number of vertices ( order) and number of edges (size)? Any reference (if possible) in this regards would also be appreciated.

• no. consider 4 vertices with 3 edges. one possibility is a triangle and an isolated vertex, which has chromatic number 3. another possibility is a square with 3 out of 4 sides, which has chromatic number 2 – mathworker21 Aug 2 at 16:23
• Try Googling "chromatic number" – saulspatz Aug 2 at 17:32