Related papers: A Sharp upper bound for the spectral radius of a n…

Let $G$ be a connected uniform hypergraphs with maximum degree $\Delta$, spectral radius $\lambda$ and minimum H-eigenvalue $\mu$. In this paper, we give some lower bounds for $\Delta-\lambda$, which extend the result of [S.M. Cioab\u{a},…

In this paper, we obtain two spectral upper bounds for the $k$-independence number of a graph which is is the maximum size of a set of vertices at pairwise distance greater than $k$. We construct graphs that attain equality for our first…

The spectra of digraphs, unlike those of graphs, is a relatively unexplored territory. In a digraph, a separation is a pair of sets of vertices X and Y such that there are no arcs from X and Y . For a subclass of eulerian digraphs, we give…

This paper gives a tight upper bound on the spectral radius of the signless Laplacian of graphs of given order and clique number. More precisely, let G be a graph of order n, let A be its adjacency matrix, and let D be the diagonal matrix…

Let $G$ be a simple connected graph of order $n$ and $\partial(G)$ is the spectral radius of the distance matrix $D(G)$ of $G$. The transmission $D_i$ of vertex $i$ is the $i$-th row sum of $D(G)$. Denote by $D_{\max}(G)$ the maximum of…

For a graph $G$, the unraveled ball of radius $r$ centered at a vertex $v$ is the ball of radius $r$ centered at $v$ in the universal cover of $G$. We obtain a lower bound on the weighted spectral radius of unraveled balls of fixed radius…

The generalized distance spectral radius of a connected graph $G$ is the spectral radius of the generalized distance matrix of $G$, defined by $$D_\alpha(G)=\alpha Tr(G)+(1-\alpha)D(G), \;\;0\le\alpha \le 1,$$ where $D(G)$ and $Tr(G)$…

In this paper, we determine the graphs whose spectral radius and distance spectral radius attain maximum and minimum among all complements of clique trees. Furthermore, we also determine the graphs whose spectral radius and distance…

A complex unit gain graph ($ \mathbb{T} $-gain graph), $ \Phi=(G, \varphi) $ is a graph where the function $ \varphi $ assigns a unit complex number to each orientation of an edge of $ G $, and its inverse is assigned to the opposite…

We derive a lower bound to the spectral threshold of the Dirichlet Laplacian in tubular neighbourhoods of constant radius about complete surfaces. This lower bound is given by the lowest eigenvalue of a one-dimensional operator depending on…

Let $A = [a_{i j}]_{i,j=1}^n$ be a nonnegative matrix with $a_{1 1} = 0$. We prove some lower bounds for the spread $s(A)$ of $A$ that is defined as the maximum distance between any two eigenvalues of $A$. If $A$ has only two distinct…

We give an upper bound on the largest eigenvalue of a graph of given order, size, and girth.

We give upper and lower bounds on the spectral radius of a graph in terms of the number of walks. We generalize a number of known results.

We consider the problem of finding universal bounds of "isoperimetric" or "isodiametric" type on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at the vertices, in terms of various analytical and…

Shiu, Chan and Chang [On the spectral radius of graphs with connectivity at most $k$, J. Math. Chem., 46 (2009), 340-346] studied the spectral radius of graphs of order $n$ with $\kappa(G) \leq k$ and showed that among those graphs, the…

We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for real-valued potentials. For $L^1$-potentials, we obtain optimal…

In distributed optimization or Nash-equilibrium seeking over directed graphs, it is crucial to find a matrix norm under which the disagreement of individual agents' states contracts. In existing results, the matrix norm is usually defined…

For a connected graph $G$, the distance Laplacian spectral radius of $G$ is the spectral radius of its distance Laplacian matrix $\mathcal{L}(G)$ defined as $\mathcal{L}(G)=Tr(G)-D(G)$, where $Tr(G)$ is a diagonal matrix of vertex…

Let $\mathcal{G}_{n, \beta^*}$ $(\mathcal{G}^*_{n,\beta^*})$ be the set of all (connected) graphs of order $n$ with fractional matching number $\beta^*$. In this paper, the graphs with maximal spectral radius in $\mathcal{G}_{n,\beta^*}$…

Using spectral embedding based on the signless Laplacian, we obtain bounds on the spectrum of transition matrices on graphs. As a consequence, we bound return probabilities and the uniform mixing time of simple random walk on graphs. In…