Related papers: On the Laplacian spread of digraphs

In this paper, we establish a tight sufficient condition for the Hamiltonicity of graphs with large minimum degree in terms of the signless Laplacian spectral radius and characterize all extremal graphs. Moreover, we prove a similar result…

This paper studies an open consensus network design problem: identifying the optimal simple directed graphs, given a fixed number of vertices and arcs, that maximize the second smallest real part of all Laplacian eigenvalues, referred to as…

A sign is introduced in the usual Laplacian on graphs and the corresponding analogue of the isoperimetric constant for this Laplacian is presented, i.e. a geometric quantity which enables to bound from above and below the first eigenvalue.…

We consider the normalized Laplace operator for directed graphs with positive and negative edge weights. This generalization of the normalized Laplace operator for undirected graphs is used to characterize directed acyclic graphs. Moreover,…

The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the…

We consider the problem of decomposing the edges of a digraph into as few paths as possible. A natural lower bound for the number of paths in any path decomposition of a digraph $D$ is $\frac{1}{2}\sum_{v\in V(D)}|d^+(v)-d^-(v)|$; any…

Resistance distance has been studied extensively in the past years, with the majority of previous studies devoted to undirected networks, in spite of the fact that various realistic networks are directed. Although several generalizations of…

We prove two mixed versions of the Discrete Nodal Theorem of Davies et. al. [3] for bounded degree graphs, and for three-connected graphs of fixed genus $g$. Using this we can show that for a three-connected graph satisfying a certain…

A graph is called "Laplacian integral" if the eigenvalues of its Laplacian matrix are all integers. We investigate the subset of these graphs whose Laplacian is furthermore diagonalized by a matrix with entries coming from a fixed set, in…

We give a construction of a family of (weighted) graphs that are pairwise cospectral with respect to the normalized Laplacian matrix, or equivalently probability transition matrix. This construction can be used to form pairs of cospectral…

The entropy of a digraph is a fundamental measure which relates network coding, information theory, and fixed points of finite dynamical systems. In this paper, we focus on the entropy of undirected graphs. We prove that for any integer $k$…

We consider upward-planar layered drawings of directed graphs, i.e., crossing-free drawings in which each edge is drawn as a y-monotone curve going upward from its tail to its head, and the y-coordinates of the vertices are integers. The…

It is known that every distance-regular digraph is connected and normal. An interesting question is: when is a given connected normal digraph distance-regular? Motivated by this question first we give some characterizations of weakly…

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian…

We give sharp upper bounds for the ordinary spectral radius and signless Laplacian spectral radius of a uniform hypergraph in terms of the average $2$-degrees or degrees of vertices, respectively, and we also give a lower bound for the…

For a connected graph $G$ on $n$ vertices, recall that the distance signless Laplacian matrix of $G$ is defined to be $\mathcal{Q}(G)=Tr(G)+\mathcal{D}(G)$, where $\mathcal{D}(G)$ is the distance matrix, $Tr(G)=diag(D_1, D_2, \ldots, D_n)$…

We observe that the Laplacian of a random graph G on N vertices represents and explicitly solvable model in the limit of infinitely increasing N. Namely, we derive recurrent relations for the limiting averaged moments of the adjacency…

We give several algebraic bounds for percolation on directed and undirected graphs: proliferation of strongly-connected clusters, proliferation of in- and out-clusters, and the transition associated with the number of giant components.

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…

There has been recent work [Louis STOC 2015] to analyze the spectral properties of hypergraphs with respect to edge expansion. In particular, a diffusion process is defined on a hypergraph such that within each hyperedge, measure flows from…