Generalization for Laplacian energy

【摘要】：Let G be a simple graph with n vertices and m edges.Let λ1,λ2,…,λn,be the adjacency spectrum of G,and let μ1,μ2,…,μn be the Laplacian spectrum of G.The energy n n of G is E(G) = ∑n i=1|λi|,while the Laplacian energy of G is defined as LE(G) =∑n i=1|μi - 2m |.n i=1 i=1 Let γ1,γ2,…,γn be the eigenvalues of Hermite matrix A.The energy of Hermite matrix as n HE(A) =∑n i=1 |γi - tr(A) | is defined and investigated in this paper.It is a natural generalization n i=1 of E(G) and LE(G).Thus all properties about energy in unity can be handled by HE(A).