## 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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### References:

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