Abstract:
We consider the spectral radius of signed graphs without negative even cycles and its relations with the spectral radius of signed graphs obtained by removing a vertex, removing an edge or reversing the sign of an edge. As an application, we determine signed graphs that maximize the spectral radius in the class of unicyclic signed graphs with fixed order and girth. We also give certain upper bounds on the spectral radius of unicyclic oriented graphs.
Key Words: Signed graph, adjacency matrix, largest eigenvalue, spectral radius, unicyclic graph, oriented graph.
2010 Mathematics Subject Classification: Primary 05C22; Secondary 05C50, 05C20.
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