On Graphs Determined By Their Spectrum And Angle

A graph is said to be determined by its spectrum if there is no other nonisomorphic graph with the same spectrum. Answering this problem seems out of research (including finding cospectral graphs), now. At the basis of them, In this paper, by calculating adjacency characteristic polynomial, the number of closedcircuit, using the property that bipartite graphs with same Laplacian spectrum must be Line-cospectral and the property of graphs with the same eigenvalues and angles to study some non-regular graphs with special structure.We prove that:(1)No graphs C_{(n1),(n2),(n3),(n4)} are cospectral(2)Graphs S_1,1,1,(2l+1) with l not equal 1 isn't determined by its adjacency spectrum(3)No graphs C_p,q,s are cospectral(4)The corona of C_n and K₁ with n even is determined by their Laplacian spectrum(5)Graph H_m,p,q with m even is determined by its Laplacian spectrum(6)The corona of C_n and K₁ is characterized by eigenvalues and angels(7)Graph H_m,p,q with m odd is characterized by eigenvalues and angels(8)Single wheel graph W_n+1 is characterized by eigenvalues and angels(9)The tree T_a is characterized by eigenvalues and angels(10)Graph C_m,s,s with p odd is characterized by eigenvalues and angels(11)The corona of P_n and K₁ and a kind of molecular graph of alkyl are characterized by eigenvalues and angels...