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Let G (resp. G n ) be the set of connected graphs (resp. with n vertices) whose eigenvalues are mutually distinct, and G ∗ (resp. G n ∗ ) the set of connected graphs (resp. with n vertices) whose eigenvalues are mutually distinct and main. Two graphs G and H are said to be cospectral if they share the same adjacency spectrum. In this paper, we give a new method to...
The adjacency spectrum of a graph Γ , which is denoted by S p e c ( Γ ) , is the multiset of eigenvalues of its adjacency matrix. We say that two graphs Γ and Γ ′ are cospectral if S p e c ( Γ ) = S p e c ( Γ ′ ) . In this paper for each prime number p , p ≥ 23 , we construct a large family of cospectral non-isomorphic Cayley graphs over the dihedral group of order 2 p...
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