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For a graph G with n vertices, let A(G) be its adjacency matrix and PA(G, λ) the characteristic polynomial of A(G).The set of eigenvalues of A(G) is called
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For a graph G with n vertices, let A(G) be its adjacency matrix and PA(G, λ) the characteristic polynomial of A(G).The set of eigenvalues of A(G) is called the adjacency spectrum of G.A graph is said to be determined by its adjacency spectrum (DS for short) if there is no other non-isomorphic graph with the same spectrum with respect to the adjacency matrix.In this paper, we give two parameters Π5(G) and Π6(G), which relate to characteristic polynomial of graph G.All connected graphs with Π5(G) =1, 0,-1,-2,-3 and Π6(G) =0,-1 are characterized.Some interesting properties of Π5(G) and Π6(G) are given also.By the results, we give many graphs with triangles determined by their adjacency spectrum.Furthermore, we generalize these results to graphs with odd circles.
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