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Distances Between Immersed Graphs: Metric Properties
Graphs in metric spaces appear in a wide range of data sets, and there is a large body of work focused on comparing, matching, or analyzing...
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Investigation of Statistics of Nearest Neighbor Graphs
AbstractThis paper describes some statistical properties of the nearest neighbor graphs (NNGs). We study the sample distributions of graphs by the...
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Turán Problems for Oriented Graphs
A classical Turán problem asks for the maximum possible number of edges in a graph of a given order that does not contain a particular graph H as a...
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Discussion about Properties of First Nearest Neighbor Graphs
AbstractIn this study we present a benchmark of statistical distributions of the first nearest neighbors in random graphs. We consider distribution...
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Modeling the Nearest Neighbor Graphs to Estimate the Probability of the Independence of Data
AbstractThe proposed method is based on calculations of the statistics of the nearest neighbor graph (NNG) structures, which are presented as a...
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Communicability cosine distance: similarity and symmetry in graphs/networks
A distance based on the exponential kernel of the adjacency matrix of a graph and representing how well two vertices connect to each other in a graph...
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Distances between Maximal Monotone Operators
We introduce a series of distances between maximal monotone operators and study their properties. As applications, we consider the existence of...
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The density of planar sets avoiding unit distances
By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set...
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Source detection on graphs
Spreading processes on networks (graphs) have become ubiquitous in modern society with prominent examples such as infections, rumors, excitations,...
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Ollivier Curvature of Random Geometric Graphs Converges to Ricci Curvature of Their Riemannian Manifolds
Curvature is a fundamental geometric characteristic of smooth spaces. In recent years different notions of curvature have been developed for...
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Counting Vertices in Iterated Line Graphs
We introduce new methods of studying properties of iterated line graphs and demonstrate the use of these methods on a class of tree graphs. We also...
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Universal distances for extended persistence
The extended persistence diagram is an invariant of piecewise linear functions, which is known to be stable under perturbations of functions with...
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Properties of Sierpinski Triangle Graphs
The Sierpinski triangle can be modeled using graphs in two different ways, resulting in classes of graphs called Sierpinski triangle graphs and Hanoi...
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Metric Dimension Parameterized by Treewidth in Chordal Graphs
The metric dimension has been introduced independently by Harary, Melter [11] and Slater [15] in 1975 to identify vertices of a graph G using its...
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Estimates of the Number of Edges in Subgraphs of Johnson Graphs
AbstractWe consider special distance graphs and estimate the number of edges in their subgraphs. The estimates obtained improve some known...
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Reconstruction of old maps based on old photos using fuzzy graphs
About 70 years ago, the reconstruction conjecture was proposed as an interesting problem in graph theory. In this paper, we extend the concept of...
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On Euclidean Distances and Sphere Representations
We extend recent results of Abdo Alfakih, who constructed Colin de Verdière matrices for complements of penny graphs from Euclidean distance...
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Comparison between Merrifield-Simmons Index and Wiener Index of Graphs
The Merrifield-Simmons index σ is the total number of independent vertex sets (including the empty set) of the graph G . The Wiener index W is the sum...
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Functionality of Box Intersection Graphs
Functionality is a graph complexity measure that extends a variety of parameters, such as vertex degree, degeneracy, clique-width, or twin-width. In...
