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LetGbe ak-connected irregular graph of ordern, sizemand maximum degree. Letbe the signless Laplacian spectral radius ofG. In this article, we prove the following lower bound on: Moreover, we determine similar bounds for the signless Laplacian spectral radius of proper spanning subgraphs andk-edge-connected graphs. [ABSTRACT FROM PUBLISHER]

The normalized Laplacian eigenvalues of a network play an important role in its structural and dynamical aspects associated with the network. In this paper, we consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As an example of the application, the smallest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order is determined. [ABSTRACT FROM PUBLISHER]

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. P. Hansen and D. Stevanović (2008) [9] determined the graphs with maximum spectral radius among all connected graphs of order n with diameter D . In this paper, we generalize this result to k -connected graphs of order n with diameter D . [ABSTRACT FROM AUTHOR]

In this paper, we give sufficient conditions on the spectral radius for a bipartite graph being Hamiltonian and traceable, which expand the results of Lu, Liu and Tian (2012) [10] . Furthermore, we also provide tight sufficient conditions on the signless Laplacian spectral radius for a graph to be Hamiltonian and traceable, which improve the results of Yu and Fan (2012) [11] . [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph of order n . Its normalized Laplacian eigenvalues are λ 1 ≥ λ 2 ≥ ⋯ ≥ λ n − 1 ≥ λ n = 0 . In this paper, new bounds on S β * ( G ) = ∑ i = 1 n − 1 λ i β ( β  ≠ 0, 1) are derived. [ABSTRACT FROM AUTHOR]

By the well-known Perron–Frobenius Theorem [3] , for a connected graph G , its largest eigenvalue strictly increases when an edge is added. We are interested in how the other eigenvalues of a connected graph change when edges are added. Examples show that all cases are possible: increased, decreased, unchanged. In this paper, we consider the effect on the eigenvalues by suitably adding edges in particular families, say the family of connected graphs with clusters. By using the result, we also consider the effect on the energy by suitably adding edges to the graphs of the above families. [ABSTRACT FROM AUTHOR]

We correct an error in the statements of (2) of Lemma 2.2, (2) of Corollary 2.1 and (2) of Theorem 2.1 of [Linear Algebra Appl. 548 (2018) 57–65]. [ABSTRACT FROM AUTHOR]