Pacheco, Maria F.Luz, Carlos J.Cardoso, Domingos M.2011-05-312011-05-312010Pacheco, Maria F.; Luz, Carlos J.; Cardoso, Domingos M. (2010). Algorithmic strategies for the recognition of graphs with convex quadratic stability number. In 23rd European Conference on Operational Research. Lisboahttp://hdl.handle.net/10198/4777A major difficulty in the recognition of graphs with convex quadratic stability number is the existence of adverse subgraphs (an adverse subgraph is a subgraph such that the smallest eigenvalue of its adjacency matrix doesn’t change when any vertex or the neighbourhood of any vertex is deleted). It is a challenge to find adverse graphs without convex quadratic stability number. We present the main results about graphs with convex quadratic stability number and conclusions about the existence of adverse subgraphs belonging to this family in certain classes of graphs.engConvex optimizationCombinatorial optimizationconference object