Locating eigenvalues of unicyclic graphs
Copyright policy )Locating eigenvalues of unicyclic graphs
We present a linear time algorithm that computes the number of eigenvalues of a unicyclic graph in a given real interval. It operates directly on the graph, so that the matrix is not needed explicitly. The algorithm is applied to study the multiplicities of eigenvalues of closed caterpillars, obtain the spectrum of balanced closed caterpillars and give sufficient conditions for these graphs to be non-integral. We also use our method to study the distribution of eigenvalues of unicyclic graphs formed by adding a fixed number of copies of a path to each node in a cycle. We show that they are not integral graphs.
unicyclic graphs, Eigenvalues, singular values, and eigenvectors, Graphs and linear algebra (matrices, eigenvalues, etc.), Graph algorithms (graph-theoretic aspects), closed caterpillars, localitaion of eigenvalues, unicyclic caterpillars
unicyclic graphs, Eigenvalues, singular values, and eigenvectors, Graphs and linear algebra (matrices, eigenvalues, etc.), Graph algorithms (graph-theoretic aspects), closed caterpillars, localitaion of eigenvalues, unicyclic caterpillars
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