Let B(n, g) be the class of bicyclic graphs on n vertices with girth g. In this paper, the graphs in B(n, g) with the largest signless Laplacian spectral radius are characterized.

for a simple digraph $g$ of order $n$ with vertex set${v_1,v_2,ldots, v_n}$, let $d_i^+$ and $d_i^-$ denote theout-degree and in-degree of a vertex $v_i$ in $g$, respectively. let$d^+(g)=diag(d_1^+,d_2^+,ldots,d_n^+)$ and$d^-(g)=diag(d_1^-,d_2^-,ldots,d_n^-)$. in this paper we introduce$widetilde{sl}(g)=widetilde{d}(g)-s(g)$ to be a new kind of skewlaplacian matrix of $g$, where $widetilde{d}(g...

Abstract Graphs can be associated with a matrix according to some rule and we find the spectrum of graph respect that matrix. Two graphs are cospectral if they have same spectrum. Constructions help us establish patterns about structural information not preserved by We generalize construction for previously given distance Laplacian larger family graphs. In addition, show appropriate assumptions...

The spectrum of a matrix M is the multiset that contains all the eigenvalues of M. If M is a matrix obtained from a graph G, then the spectrum of M is also called the graph spectrum of G. If two graphs has the same spectrum, then they are cospectral (or isospectral) graphs. In this paper, we compare four spectra of matrices to examine their accuracy in protein structural comparison. These four ...

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...

In this paper, we show that the eigenvectors associated with the zero eigenvalues of the Laplacian and signless Lapacian tensors of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector associated with the zero eigenvalue of the Laplacian or signless Lapacian tensor have the same modulus. Moreover, under a cano...

In this paper, we show that the eigenvectors of the zero Laplacian and signless Lapacian eigenvalues of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector of the zero Laplacian or signless Lapacian eigenvalue have the same modulus. Moreover, under a canonical regularization, the phases of the components of t...

The spectral radius (or the signless Laplacian radius) of a general hypergraph is maximum modulus eigenvalues its adjacency Laplacian) tensor. In this paper, we firstly obtain lower bound hypergraphs in terms clique number. Moreover, present relation between homogeneous polynomial and number hypergraphs. As an application, finally upper