New Bounds on the Independence Number of connected Graphs

A subset of vertices in a graph G is an independent set if it contains no edge of G. The independence number, $\alpha$(G), of G is the maximum cardinality of an independent set in G. Our main result is an improvement of a lower bound given by Henning and Lowenstein (2014) for the independence number of a connected graph. We present an improved lower bound for the independence number of a graph G in terms of its order and size when G does not belong to a specific family of graphs. We also characterize all connected graphs achieving equality for the new bound