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Laplacian spectral characterization of some graphs obtained by product operation. (English) Zbl 1242.05170

Summary: A graph is said to be DLS, if there is no other non-isomorphic graph with the same Laplacian spectrum. Let \(G\) be a DLS graph. We show that \(G\times K_{r}\) is DLS if \(G\) is disconnected. If \(G\) is connected, it is proved that \(G\times K_{r}\) is DLS under certain conditions. Applying this result, we prove that \(G\times K_{r}\) is DLS if \(G\) is a tree on \(n(n\geq 5)\) vertices or a unicyclic graph on \(n(n\geq 6)\) vertices.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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