Abstract
Let K n m denote the graph obtained by attaching m pendent edges to a vertex of complete graph K n - m , and U n , p the graph obtained by attaching n - p pendent edges to a vertex of C p . In this paper, we first prove that the graph K n m and its complement are determined by their adjacency spectra, and by their Laplacian spectra. Then we prove that U n , p is determined by its Laplacian spectrum, as well as its adjacency spectrum if p is odd, and find all its cospectral graphs for U n , 4 .
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