Related papers: Uniqueness of a solution to a general class of dis…

In this short note, we prove the uniqueness of exterior differentiation on locally finite graphs.

We study graph-directed conjugate functional equations on the unit interval indexed by the complete digraph with self-loops on two vertices. We focus on the singularity and regularity of the solutions for compatible systems of weak…

In this work we address graph based semi-supervised learning using the theory of the spatial segregation of competitive systems. First, we define a discrete counterpart over connected graphs by using direct analogue of the corresponding…

We show that if a group can be represented as a graph product of finite directly indecomposable groups, then this representation is unique.

In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold…

Motivated by applications in data science, we study partial differential equations on graphs. By a classical fixed-point argument, we show existence and uniqueness of solutions to a class of nonlocal continuity equations on graphs. We…

We study the uniqueness of solutions to a class of heat equations with positive density posed on infinite weighted graphs. We separately consider the case when the density is bounded from below by a positive constant and the case of…

We derive integrable discrete systems which are contiguity relations of two equations in the Painlev\'e-Gambier classification depending on some parameter. These studies extend earlier work where the contiguity relations for the six…

This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably,…

We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show…

In this paper we give an elementary proof of uniqueness of solutions to a gas-disk interaction system with diffusive boundary condition. Existence of near-equilibrium solutions for this type of systems with various boundary conditions has…

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse…

Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…

Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…

A theory about the implication structure in graph coloring is presented. Discovering hidden relations is a crucial activity in every scientific discipline. The development of mathematical models to study and discover such hidden relations…

The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…

We prove the uniqueness of the infinite connected component for the vacant set of random interlacements on general vertex-transitive amenable transient graphs. Our approach is based on connectedness of random interlacements and differs from…

We prove that a connected simplicial complex is uniquely determined by its complex of discrete Morse functions. This settles a question raised by Chari and Joswig. In the 1-dimensional case, this implies that the complex of rooted forests…

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…

In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are…