Related papers: The Signless Laplacian Matrix of Hypergraphs
A new class of isospectral graphs is presented. These graphs are isospectral with respect to both the normalised Laplacian on the discrete graph and the standard differential Laplacian on the corresponding metric graph. The new class of…
In this paper, the Laplacian characteristic polynomial of uniform hypergraphs with cut vertices or pendant edges and the Laplacian matching polynomial of uniform hypergraphs are characterized.The multiplicity of the zero Laplacian…
In this paper, we investigate some relations between the invariants (including vertex and edge connectivity and forwarding indices) of a graph and its Laplacian eigenvalues. In addition, we present a sufficient condition for the existence…
We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…
In this article, we relate the spectrum of the discrete magnetic Laplacian (DML) on a finite simple graph with two structural properties of the graph: the existence of a perfect matching and the existence of a Hamiltonian cycle of the…
Let $\mathcal{H}=(V, E)$ be an $r$-uniform hypergraph on $n$ vertices. The signless Laplacian spectral radius of $\mathcal{H}$ is defined as the maximum modulus of the eigenvalues of the tensor…
This paper surveys some recent results and progress on the extremal prob- lems in a given set consisting of all simple connected graphs with the same graphic degree sequence. In particular, we study and characterize the extremal graphs…
This paper gives tight upper bound on the largest eigenvalue q(G) of the signless Laplacian of graphs with no paths of given order. The main ingredient of our proof is a stability result of its own interest, about graphs with large minimum…
Let $G$ be a simple, connected graph, $\mathcal{D}(G)$ be the distance matrix of $G$, and $Tr(G)$ be the diagonal matrix of vertex transmissions of $G$. The distance Laplacian matrix and distance signless Laplacian matrix of $G$ are defined…
We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition of a fixed total edge length, the configurations for which…
A $k$-cyclic graph is a connected graph of order $n$ and size $n+k-1$. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all $C_{4}$-free $k$-cyclic graphs of order $n$.…
Given a graph Laplacian with positively and negatively weighted edges we are interested in characterizing the set of weights that give a particular spectral index, i.e.~give a prescribed number of positive, zero, and negative eigenvalues.…
This paper is devoted to the investigation of the spectral theory and dynamical properties of periodic graphs which are not locally finite but carry non-negative, symmetric and summable edge weights. These graphs are shown to exhibit rather…
In this paper, we introduce a generalization of corona of graphs. This construction generalizes the generalized corona of graphs (consequently, the corona of graphs), the cluster of graphs, the corona-vertex subdivision graph of graphs and…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Let $G$ be a connected simple graph of order $n$. Let $\rho_1(G)\geq \rho_2(G)\geq \cdots \geq \rho_{n-1}(G)> \rho_n(G)=0$ be the eigenvalues of the normalized Laplacian matrix $\mathcal{L}(G)$ of $G$. Denote by $m(\rho_i)$ the multiplicity…
Let $G$ be a connected graph with vertex set $V(G)$ and edge set $E(G)$. Let $Tr(G)$ be the diagonal matrix of vertex transmissions of $G$ and $D(G)$ be the distance matrix of $G$. The distance Laplacian matrix of $G$ is defined as…
As a bridge connecting the matching polynomial and the Laplacian matching polynomial of graphs, the subdivision method is expected to be useful for investigating the Laplacian matching polynomial. In this paper, we study applications of the…
We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In…
The graph entropy describes the structural information of graph. Motivated by the definition of graph entropy in general graphs, the graph entropy of hypergraphs based on Laplacian degree are defined. Some results on graph entropy of simple…