Generalization for Laplacian energy

作者：Liu Jian ping; Liu Bo lian^*

来源：Applied Mathematics-A Journal of Chinese Universities Series B, 2009, 24(4): 443-450.

DOI：10.1007/s11766-009-2165-5

• energy (of matrix)
• Hermite matrix
• eigenvalue

Let G be a simple graph with n vertices and m edges. Let lambda(1), lambda(2), ... , lambda(n), be the adjacency spectrum of G, and let mu(1), mu(2), ... , mu(n) be the Laplacian spectrum of G. The energy of G is E(G) = Sigma(n)(i=1) vertical bar lambda(i)vertical bar, while the Laplacian energy of G is defined as LE(G) = Sigma(n)(i=1) vertical bar mu(i) - 2m/n vertical bar. Let gamma(1), gamma(2), ... , gamma(n) be the eigenvalues of Hermite matrix A. The energy of Hermite matrix as LE(A) = Sigma(n)(i=1)vertical bar gamma(i) - tr(A)/n vertical bar is defined and investigated in this paper. It is a natural generalization of E(G) and LE(G). Thus all properties about energy in unity can be handled by HE(A).

• 出版日期2009-12
• 单位华南师范大学; 福州大学