Related papers: Effective Resistance in Simplicial Complexes as Bi…
Effective Field Theory (EFT) stands as a cornerstone in modern theoretical physics, offering a powerful framework for describing the dynamics of physical systems across a wide range of energy scales. This article provides an in-depth…
By means of an envelope function analysis, we perform a numerical investigation of the conductance behavior of a graphene structure consisting of two regions (dots) connected to the entrance and exit leads through constrictions and…
We introduce and investigate a new notion of resilience in graph spanners. Let $S$ be a spanner of a graph $G$. Roughly speaking, we say that a spanner $S$ is resilient if all its point-to-point distances are resilient to edge failures.…
In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some relationship between Laplacian matrix and resistance…
We prove measurable analogues of Whitney's classical theorems on weak isomorphisms of finite graphs. In the setting of locally finite graphings, we introduce a notion of weak isomorphism as an edge-measure-preserving Borel bijection that…
We provide proofs certifying that the structure theorem for vertex sets of bounded bidimensionality holds with polynomial bounds. The bidimensionality of vertex sets is a common generalisation of both treewidth and the face-cover-number of…
Suppose we have an arrangement $\mathcal{A}$ of $n$ geometric objects $x_1, \dots, x_n \subseteq \mathbb{R}^2$ in the plane, with a distinguished point $p_i$ in each object $x_i$. The generalized transmission graph of $\mathcal{A}$ has…
It is well known that in many real networks, such as brain networks and scientific collaboration networks, there exist higher-order nonpairwise relations among nodes, i.e., interactions between among than two nodes at a time. This…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
The problem of definition of effective material parameters (permittivity and permeability) for composite layers containing only one-two parallel arrays of complex-shaped inclusions is discussed. Such structures are of high importance for…
Barrett et al studied resistance labels of electrical circuits whose underlying graphs when embedded in the Cartesian plane has the form of an $n$-grid, $n$ rows of upright triangles. Proofs in Barrett introduced a row-reduction algorithm…
In this paper, we study the construction and transformation of two-dimensional persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations,…
In Refs.[1] and [2], calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on the stratification of the network and Stieltjes function associated with the…
Effective conductivity of a 2D random composite is expressed in the form of long series in the volume fraction of ideally conducting disks. The problem of a {\it direct} reconstruction of the critical index for superconductivity from the…
Persistent homology is a fundamental tool in topological data analysis; however, it lacks methods to quantify the fragility or fineness of cycles, anticipate their formation or disappearance, or evaluate their stability beyond persistence.…
In this paper, we study two applications of graph minor reduction. In the first part of the paper, we introduce a variant of the boxicity, called strong boxicity, where the rectangular representation satisfies an additional condition that…
This paper discusses generalized weak rigidity theory, and aims to apply the theory to formation control problems with a gradient flow law. The generalized weak rigidity theory is utilized in order that desired formations are characterized…
We develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: 'space barriers' from convex…
A spanning 2-forest separating vertices $u$ and $v$ of an undirected connected graph is a spanning forest with 2 components such that $u$ and $v$ are in distinct components. Aside from their combinatorial significance, spanning 2-forests…
We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the…