Related papers: Distance spectral radius of uniform hypergraphs

In this article we introduce a definition of k-uniform thresholds hypergraphs through a binary sequence, a natural extension of the classical definition for thresholds graphs. We characterize some of its eigenvalues and multiplicities by…

It is well-known that the spectral radius of a connected uniform hypergraph is an eigenvalue of the hypergraph. However, its algebraic multiplicity remains unknown. In this paper, we use the Poisson Formula and matching polynomials to…

Let $G$ be a graph with adjacency matrix $A(G)$, and let $D(G)$ be the diagonal matrix of the degrees of $G$. For any real $\alpha\in[0,1]$, write $A_\alpha(G)$ for the matrix $$A_\alpha(G)=\alpha D(G)+(1-\alpha)A(G).$$ This paper presents…

The unit-distance graph on the $n$-dimensional integer lattice $\mathbb{Z}^n$ is called the $n$-dimensional grid. We attempt to maximize the girth of a $k$-regular (possibly induced) subgraph of the $n$-dimensional grid, and provide…

Let $G$ be a simple connected graph, and $D(G)$ be the distance matrix of $G$. Suppose that $D_{\max}(G)$ and $\lambda_1(G)$ are the maximum row sum and the spectral radius of $D(G)$, respectively. In this paper, we give a lower bound for…

Let $\mathcal{G}(m,k)$ be the set of graphs with size $m$ and odd girth (the length of shortest odd cycle) $k$. In this paper, we determine the graph maximizing the spectral radius among $\mathcal{G}(m,k)$ when $m$ is odd. As byproducts, we…

We study random graphs with arbitrary distributions of expected degree and derive expressions for the spectra of their adjacency and modularity matrices. We give a complete prescription for calculating the spectra that is exact in the limit…

In this paper, we give the relationship between spectral radius and local structures of graphs and hypergraphs. Our work shows that certain local subgraphs (subhypergraphs) must occur when the spectral radius ratio is large. We also give…

In this paper, some special distance spectral properties of graphs are considered. Concretely, we recursively construct an infinite family of trees with distance eigenvalue $-1$, and determine all $\{C_3,C_4\}$-free connected graphs with…

Let G be a simple undirected connected graph. In this paper, new upper bounds on the distance Laplacian spectral radius of G are obtained. Moreover, new lower and upper bounds for the distance signless Laplacian spectral radius of G are…

We investigated Raman spectra of single-layer and multi-layer graphene under ultraviolet laser excitation at the wavelength of 325 nm. It was found that while the G peak of graphene remains pronounced in UV Raman spectra, the 2D band…

Let $\mathcal T (n, k)$ be the set of the $k$-uniform supertrees with $n$ vertices and $m$ edges, where $k\geq 3$, $n\geq 5$ and $m=\frac{n-1}{k-1}$. % Let $m$ be the number of the edges of the supertrees in $\mathcal T (n, k)$, where…

In this paper we compute the spectrum of a special block matrix and use it to describe the distance spectra of some double join of graphs. As an application, we give several families of distance equienergetic graphs of diameter 3.

In this paper, we give upper and lower bounds for the spectral radius of a nonnegative irreducible matrix and characterize the equality cases. These bounds theoretically improve and generalize some known results of Duan et al.[X. Duan, B.…

We define $k$-dimensional digraphs and initiate a study of their spectral theory. The $k$-dimensional digraphs can be viewed as generating graphs for small categories called $k$-graphs. Guided by geometric insight, we obtain several new…

In this paper, we investigate various algebraic and graph theoretic properties of the distance matrix of a graph. Two graphs are $D$-cospectral if their distance matrices have the same spectrum. We construct infinite pairs of $D$-cospectral…

This paper presents sufficient conditions for Hamiltonian paths and cycles in graphs. Letting $\lambda\left( G\right) $ denote the spectral radius of the adjacency matrix of a graph $G,$ the main results of the paper are: (1) Let $k\geq1,$…

Various properties of a hypergraph can be explored through its spectrum. In this paper,we estimate the bound for the sum of $t,\,t\in[1,n]$, largest eigenvalues of a $k$-uniform hypergraph of order $n$. Also, we characterize the $k$-uniform…

We show that the kite graph $K_4^{(n)}$ uniquely maximizes the distance spectral radius among all connected $4$-chromatic planar graphs on $n$ vertices.

In this paper, we study dual quaternion and dual complex unit gain graphs and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications…