【摘 要】
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Let G be a graph with adjacency matrix A and diagonal degree matrix D.The eigenvalues of G are the eigenvalues of A.Let εA(λ) ={x ∈ Rn | Ax =λx} be the eige
【机 构】
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XinjiangUniversity,Xinjiang,China
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Let G be a graph with adjacency matrix A and diagonal degree matrix D.The eigenvalues of G are the eigenvalues of A.Let εA(λ) ={x ∈ Rn | Ax =λx} be the eigenspace of λ.We call λ a main eigenvalue of G if there exists x ∈ εA(λ) such that x is not orthogonal to all-one vector e, i.e., xTe ≠ 0.Otherwise, λ is a non-main eigenvalue.The Laplacian and Signless Laplacian eigenvalues of G are, respectively, the eigenvalues of Laplacian matrix L =D-A and Signless Laplacian matrix L =D + A.Their main and non-main eigenvalues are similarly defined.
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