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Which wheel graphs are determined by their Laplacian spectra? (English) Zbl 1189.05111

Summary: The wheel graph, denoted by \(W_{n+1}\), is the graph obtained from the circuit \(C_n\) with \(n\) vertices by adding a new vertex and joining it to every vertex of \(C_n\). In this paper, the wheel graph \(W_{n+1}\), except for \(W_{7}\), is proved to be determined by its Laplacian spectrum, and a graph cospectral with the wheel graph \(W_{7}\) is given.

MSC:

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