Given a commutative ring R with identity 1≠ 0, let the set Z (R) denote the set of zero-
divisors and let Z*(R)= Z (R)\{0} be the set of non-zero zero-divisors of R. The zero-divisor …

Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and
eigenvectors of matrices associated with graphs to study them. In this paper, we present a …

The reciprocal distance Laplacian matrix of a connected graph G is defined as RDL (G)= RT
(G)− RD (G), where RT (G) is the diagonal matrix of reciprocal distance degrees and RD (G) …

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 …

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 connected simple graph G, the generalized distance matrix is defined by D α:= α T r
(G)+(1-α) D (G), 0≤ α≤ 1, where Tr (G) is the diagonal matrix of vertex transmissions and D …

For a simple graph $ G (V, E) $ with $ n $ vertices, $ m $ edges, vertex set $ V (G)=\{v_1,
v_2,\dots, v_n\} $ and edge set $ E (G)=\{e_1, e_2,\dots, e_m\} $, the adjacency matrix …

Brouwer's Conjecture states that, for any graph G, the sum of the k largest (combinatorial)
Laplacian eigenvalues of G is at most| E (G)|+(k+ 1 2), 1≤ k≤ n. We present several …

For a simple graph G with order n and size m having Laplacian eigenvalues μ _1, μ _2,\dots,
μ _ n-1, μ _n= 0 μ 1, μ 2,⋯, μ n-1, μ n= 0, let S_k (G)= ∑ _ i= 1^ k μ _i S k (G)=∑ i= 1 k μ i, be …

Let $ G $ be a connected graph with $ n $ vertices, $ m $ edges and having diameter $ d $.
The distance Laplacian matrix $ D^{L} $ is defined as $ D^ L= $ Diag $(Tr)-D $, where Diag …