Related papers: Elastic Graphs
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
The energy of a graph $G$, denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of $G$. Let $G$ be a graph of order $n$ and ${\rm rank}(G)$ be the rank of the adjacency matrix of $G$. In this paper we…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technology. An important characteristic of such materials is their…
In the study of neurons, morphology influences function. The complexity in the structure of neurons poses a challenge in the identification and analysis of similar and dissimilar neuronal cells. Existing methodologies carry out structural…
Let G be a simple graph on n vertices with vertex set V(G). The energy of G, denoted by, $\mathcal{E}(G)$ is the sum of all absolute values of the eigenvalues of the adjacency matrix $A(G)$. It is the first eigenvalue-based topological…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix $\c$, and the relevant statistical ensembles are defined in terms of a partition function $Z=\sum_{\c} \exp {[}-\beta \H(\c)…
In this paper, we mainly study the trace norm of the adjacency matrix of a graph, also known as the energy of graph. We give the maximum trace norms for the graph and its complement. In fact, the above problem is stated and solved in a more…
Given a set of points in the plane, we want to establish a connection network between these points that consists of several disjoint layers. Motivated by sensor networks, we want that each layer is spanning and plane, and that no edge is…
The edge-bandwidth of a graph is the minimum, over all labelings of the edges with distinct integers, of the maximum difference between labels of two incident edges. We prove that edge-bandwidth is at least as large as bandwidth for every…
The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity…
A graph is 1-planar if it can be drawn in the plane so that each edge is crossed at most once. However, there are 1-planar graphs which do not admit a straight-line 1-planar drawing. We show that every 1-planar graph has a straight-line…
The choice of elastic energies for thin plates and shells is an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four…
We establish a lower bound for the energy of a complex unit gain graph in terms of the matching number of its underlying graph, and characterize all the complex unit gain graphs whose energy reaches this bound.
The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in…
In the emerging field of mechanical metamaterials, using periodic lattice structures as a primary ingredient is relatively frequent. However, the choice of aperiodic lattices in these structures presents unique advantages regarding failure,…
We interpret the subgraph centrality as the partition function of a network. The entropy, the internal energy and the Helmholtz free energy are defined for networks and molecular graphs on the basis of graph spectral theory. Various…
We propose a class of networks which can be regarded as an extension of the graphitic network. These networks are constructed so that surface states with non-bonding character (edge states) are formed in a tight-binding model with one…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…