Variable neighborhood search for extremal graphs. 21. Conjectures and results about the independence number

A set of vertices SS in a graph GG is independent if no neighbor of a vertex of SS belongs to SS. The independence number αα is the maximum cardinality of an independent set of GG. A series of best possible lower and upper bounds on αα and some other common invariants of GG are obtained by the system AGX 2, and proved either automatically or by hand. In the present paper, we report on such lower and upper bounds considering, as second invariant, minimum, average and maximum degree, diameter, radius, average distance, spread of eccentricities, chromatic number and matching number.