Tura, Eigenvalues and energy in threshold graphs, Linear Algebra Appl. 465 (2015) 412-425.D.P. Jacobs, V. Trevisan, F. Tura, Eigenvalues and energy in threshold graphs, Linear Algebra Appl. 465 (2015) 412-425.D.
In Section 3, the bounds obtained for Sσ(G) are applied to obtain the lower and upper bounds for the Laplacian energy LE(G) of a graph G in terms of number of vertices n, number of edges m, maximum degree Δ and clique number ω of the graph G. These bounds improve some well ...
Tura, Eigenvalues and energy in threshold graphs, Linear Algebra Appl. 465 (2015) 412-425.D.P. Jacobs, V. Trevisan, F. Tura, Eigenvalues and energy in threshold graphs, Linear Algebra Appl. 465 (2015) 412-425.D. Jacobs, V. Trevisan, F. Tura, Eigenvalues and energy in threshold ...
threshold graphtransmission regular graphSPECTRUMENERGYSUMLet G be a simple connected graph with n vertices, m edges and having distance signless Laplacian eigenvalues ρ1≥ρ2≥…≥ρn≥0. For 1≤k≤n, let Mk(G)=∑i=1kρi and Nk(G)=∑i=0k1ρni be respectively the sum of k-largest...
,n. We obtain upper bounds for Sk(G) in terms of the clique number ω, the vertex covering number τ and the diameter d of a graph G. We show that Brouwer's conjecture holds for certain classes of graphs. The Laplacian energy LE(G) of a graph G is defined as LE(G)=∑i=1n|...
In particular, it holds for threshold graphs [5]. The conjecture holds for regular graphs [6]. For the case where 𝑘=1k=1, Conjecture 1 is derived from the inequality 𝜇1(𝐺)≤𝑛μ1(G)≤n (see [4]). In [7], the authors found that for any tree and when k is equal to...
In particular, it holds for threshold graphs [5]. The conjecture holds for regular graphs [6]. For the case where 𝑘=1k=1, Conjecture 1 is derived from the inequality 𝜇1(𝐺)≤𝑛μ1(G)≤n (see [4]). In [7], the authors found that for any tree and when k is equal to...