ON TWO LAPLACIAN-SPECTRUM-BASED GRAPH INVARIANTS AND THEIR RELATION: A REVIEW

摘要

Let G be a connected graph of order n, and let mu(1) >= mu(2) >= ... >= mu(n-1) > mu(n) = 0 be the eigenvalues of its Laplacian matrix. Then the Kirchhoff index and the Laplacian-energy-like invariant are defined as Kf = Sigma(n-1)(i=1) 1/mu(i) and LEL = Sigma(n)(i=1) root mu(i) respectively. We outline the basic details of the mathematical theory of Kf and LEL, and then consider the relations between Kf and LEL.