Abstract
Let ϕ ( G , λ ) be the characteristic polynomial of a graph G . Two graphs G and H are cospectral, denoted by G ∼ H , if ϕ ( G , λ ) = ϕ ( H , λ ) . By [ G ] ϕ we denote the cospectral equivalence class determined by G under “ ∼ ”. A graph G is said to be determined by its spectrum (or simply G is a DS-graph) if H ≅ G whenever H ∼ G . In this paper, we determine the cospectral equivalence classes of three kinds of graphs having an isolated vertex, find several DS-graphs and identify the graph that has the fourth minimum index among all connected graphs with n vertices.
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