Let G be a simple connected graph with n vertices, m edges and having distance signless
Laplacian eigenvalues ρ 1≥ ρ 2≥…≥ ρ n≥ 0. For 1≤ k≤ n, let M k (G)=∑ i= 1 k ρ i and N …

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

Let G be a simple connected graph and let S k (G) be the sum of the first k largest Laplacian
eigenvalues of G. It was conjectured by Brouwer in 2006 that S k (G)≤ e (G)+(k+ 1 2) holds …

Let G be a simple graph with order n and size m. The quantity M 1 (G)=∑ i= 1 ndvi 2 is
called the first Zagreb index of G, where dvi is the degree of vertex vi, for all i= 1, 2,⋯, n. The …

We consider the skew Laplacian matrix of a digraph G→ obtained by giving an arbitrary
direction to the edges of a graph G having n vertices and m edges. We obtain an upper …

For a simple graph G with n vertices and m edges, let D (G)= diag (d 1, d 2,⋯, dn) be its
diagonal matrix, where di= deg (vi), for all i= 1, 2,⋯, n and A (G) be its adjacency matrix. The …

‎‎ For a simple connected graph $ G $ with $ n $ vertices and $ m $ edges‎,‎ let
$\overrightarrow {G} $ be a digraph obtained by giving an arbitrary direction to the edges of …

Let G be a simple graph with n vertices. For 1≤ k≤ n, denote by S k (G) the sum of k largest
Laplacian eigenvalues of G. It is conjectured by Brouwer that S k (G)≤ e (G)+(k+ 1 2), where …