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Algorithmic strategies for the recognition of graphs with convex quadratic stability number

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Bibliographic Details
Summary:A 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.
Main Authors:Pacheco, Maria F.
Other Authors:Luz, Carlos J.; Cardoso, Domingos M.
Subject:Convex optimization Combinatorial optimization
Year:2010
Country:Portugal
Document type:conference output
Access type:open access
Associated institution:Instituto Politécnico de Bragança
Language:English
Origin:Biblioteca Digital do IPB
Description
Summary:A 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.