Let G be a simple graph with n vertices, m edges, maximum degree Δ, average degree d‾= 2
mn, clique number ω having Laplacian eigenvalues μ 1, μ 2,…, μ n− 1, μ n= 0. For k (1≤ k≤ …

For a simple graph G of order n, size m and with signless Laplacian eigenvalues q 1, q 2,…,
qn, the signless Laplacian energy QE (G) is defined as QE (G)=∑ i= 1 n| qi− d‾|, where d‾= 2 …

Let G be a graph with n vertices and m edges. Also let μ 1, μ 2,…, μ n− 1, μ n= 0 be the
eigenvalues of the Laplacian matrix of graph G. The Laplacian energy of the graph G is …

For a simple graph G with n-vertices, m edges and having Laplacian eigenvalues μ 1, μ 2,…,
μ n− 1, μ n= 0, let S k (G)=∑ i= 1 k μ i, be the sum of k largest Laplacian eigenvalues of G …

Several approaches for ordering graphs by spectral parameters are presented in the
literature. We can find graph orderings either by the greatest eigenvalue (spectral radius or …

ENERGIES OF GRAPHS SURVEY, CENSUS, BIBLIOGRAPHY Ivan Gutman & Boris Furtula
Page 1 ENERGIES OF GRAPHS SURVEY, CENSUS, BIBLIOGRAPHY Ivan Gutman & Boris …

For G being a graph with n vertices and m edges, and with Laplacian eigenvalues μ 1≥ μ
2≥⋯≥ μ n− 1≥ μ n= 0, the Laplacian energy is defined as LE=∑ i= 1 n| μ i− 2 m/n|. Let σ …

We prove that Brouwer's conjecture holds for certain classes of graphs. We also give upper
bounds for the sum of the largest Laplacian eigenvalues for graphs satisfying certain …

We study the Laplacian and the signless Laplacian energy of connected unicyclic graphs,
obtaining a tight upper bound for this class of graphs. We also find the connected unicyclic …

We study the problem of determining the graph with n vertices having largest signless
Laplacian energy. We conjecture it is the complete split graph whose independent set has …