In this paper, we determine the graph with maximal signless Laplacian spectral radius among all connected graphs with fixed order and given number of cut vertices.

In this paper, we define duplication corona, duplication neighborhood corona and duplication edge corona of two graphs. We compute their adjacency spectrum, Laplacian spectrum and signless Laplacian. As an application, our results enable us to construct infinitely many pairs of cospectral graphs and also integral graphs.

In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.

For a connected graph G on n vertices, recall that the reciprocal distance signless Laplacian matrix of is defined to be RQ(G)=RT(G)+RD(G), where RD(G) matrix, RT(G)=diag(RT1,RT2,⋯,RTn) and RTi degree vertex vi. In 2022, generalized which by RDα(G)=αRT(G)+(1−α)RD(G),α∈[0,1], was introduced. this paper, we give some bounds spectral radius RDα(G) characterize its extremal graph. addition, also li...

Recently, Braunstein et al. [1] introduced normalized Laplacian matrices of graphs as density matrices in quantum mechanics and studied the relationships between quantum physical properties and graph theoretical properties of the underlying graphs. We provide further results on the multipartite separability of Laplacian matrices of graphs. In particular, we identify complete bipartite graphs wh...

<abstract><p>Let $ A(G) and D(G) be the adjacency matrix degree diagonal of a graph G $, respectively. For any real number \alpha \in[0, 1] Nikiforov defined A_{\alpha} $-matrix as A_{\alpha}(G) = D(G)+(1-\alpha)A(G) $. Let S_k(A_{\alpha}(G)) sum k largest eigenvalues In this paper, some bounds on are obtained, which not only extends results signless Laplacian matrix, but it also gi...

Product graphs have been gainfully used in literature to generate mathematical models of complex networks which inherit properties of real networks. Realizing the duplication phenomena imbibed in the definition of corona product of two graphs, we define corona graphs. Given a small simple connected graph which we call basic graph, corona graphs are defined by taking corona product of the basic ...