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Extremal unicyclic graphs with minimal distance spectral radius. (English) Zbl 1303.05092

Summary: The distance spectral radius \(\rho(G)\) of a graph \(G\) is the largest eigenvalue of the distance matrix \(D(G)\). Let \(\mathcal U(n,m)\) be the class of unicyclic graphs of order \(n\) with given matching number \(m\) (\(m \neq 3\)). In this paper, we determine the extremal unicyclic graph which has minimal distance spectral radius in \(\mathcal U (n,m) \setminus C_n\).

MSC:

05C35 Extremal problems in graph theory
05C12 Distance in graphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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