相关论文: Laplacian Controllability of Interconnected Graphs

In this paper, we establish the relation between classic invariants of graphs and their integer Laplacian eigenvalues, focusing on a subclass of chordal graphs, the strictly chordal graphs, and pointing out how their computation can be…

The independent domination number $i(G)$ of a graph $G$ is the minimum cardinality of a maximal independent set of $G$, also called an $i(G)$-set. The $i$-graph of $G$ is the graph whose vertices correspond to the $i(G)$-sets, and where two…

Token graphs, or symmetric powers of graphs, see \cite{alavi2002survey} and \cite{Fabila-Monroy2012}, are defined on the $k$-combinations of the vertex set of some graph $L$, where edges exist between two such combinations, if their…

The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. First, a class of directed signed graphs is investigated in which one pair of nodes (either connected or not) is…

We introduce a principled generative framework for graph signals that enables explicit control of feature heterophily, a key property underlying the effectiveness of graph learning methods. Our model combines a Lipschitz graphon-based…

In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…

There are two main notions of a Laplacian operator associated with graphs: discrete graph Laplacians and continuous Laplacians on metric graphs (widely known as quantum graphs). Both objects have a venerable history as they are related to…

In this paper, several necessary and sufficient graphical conditions are derived for the controllability of multi-agent systems by taking advantage of the proposed concept of controllability destructive nodes. A key step of arriving at this…

In this paper, we study structural controllability of a linear time invariant (LTI) composite system consisting of several subsystems. We assume that the neighbourhood of each subsystem is unconstrained, i.e., any subsystem can interact…

This paper characterizes the graphical properties of an optimal topology with minimal Laplacian energy under the constraint of fixed numbers of vertices and edges, and devises an algorithm to construct such connected optimal graphs. These…

We consider modified Laplacian matrices of graphs, obtained by adding the identity matrix to the Laplacian matrix $L_G$ of a graph $G$. This results in a positive definite matrix $\tilde{L}_G$. The inverse of $\tilde{L}_G$ is a doubly…

Graphs can be associated with a matrix according to some rule and we can find the spectrum of a graph with respect to that matrix. Two graphs are cospectral if they have the same spectrum. Constructions of cospectral graphs help us…

This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…

In the past two decades, the field of applied finance has tremendously benefited from graph theory. As a result, novel methods ranging from asset network estimation to hierarchical asset selection and portfolio allocation are now part of…

A (finite or infinite) graph is called constructible if it may be obtained recursively from the one-point graph by repeatedly adding dominated vertices. In the finite case, the constructible graphs are precisely the cop-win graphs, but for…

A metrized graph is a finite weighted graph whose edges are thought of as line segments. In this expository paper, we study the Laplacian operator on a metrized graph and some important functions related to it, including the ``j-function'',…

Starting with an isolated vertex, here we construct a threshold hypergraph by repeatedly adding an isolated vertex or a $k$-dominating vertex set. We represent a threshold hypergraph by a string of non-negative integers and find the…

It is reported that dynamical systems over digraphs have superior performance in terms of system damping and tolerance to time delays if the underlying graph Laplacian has a purely real spectrum. This paper investigates the topological…

The vertex connectivity of a graph $G$ is the size of the smallest set of vertices $S$ such that $G \setminus S$ is disconnected. For the class of planar graphs, the problem of vertex connectivity is well-studied, both from structural and…

Exact controllability for the wave equation on a metric graph consisting of a cycle and two attached edges is proven. One boundary and one internal control are used. At the internal vertices, delta-prime conditions are satisfied. As a…