Extremal Graph Theory for Metric Dimension and Diameter [PDF]
Electronic Notes in Discrete Mathematics, 2007 A set of vertices $S$ resolves a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The metric dimension of $G$ is the minimum cardinality of a resolving set of $G$. Let ${\cal G}_{\beta,D}$ be the set of graphs with metric dimension $\beta$ and diameter $D$.
Hernando Martín, María del Carmen +4 more
openaire +7 more sources
Patched Network and Its Vertex-Edge Metric-Based Dimension
IEEE Access, 2023 The p-type networks are designed with the help of CVNET at topo group Cluj and also given support by nano studio. Such networks develop new p-type surfaces and also represent the decorations of the surfaces.
Sidra Bukhari +3 more
doaj +2 more sources
Analysis of Resting-State fMRI Topological Graph Theory Properties in Methamphetamine Drug Users Applying Box-Counting Fractal Dimension [PDF]
Basic and Clinical Neuroscience Journal, 2017 Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo. Of all methods to measure the functional connectivity between regions, Linear Correlation (LC) calculation of activity time series of the brain regions as a linear measure is considered the most ubiquitous one.
Meysam Siyah Mansoory +3 more
openaire +4 more sources
Neutrosophic Graphs: A New Dimension To Graph Theory
, 2015 In this book authors for the first time have made a through study of neutrosophic graphs. This study reveals that these neutrosophic graphs give a new dimension to graph theory. The important feature of this book is it contains over 200 neutrosophic graphs to provide better understanding of this concepts.
W. B. Vasantha Kandasamy +2 more
openaire +2 more sources
Metric and Fault-Tolerant Metric Dimension of Hollow Coronoid
IEEE Access, 2021 Coronoid systems actually arrangements of hexagons into six sides of benzenoids. By nature, it is an organic chemical structure. Hollow coronoids are primitive and catacondensed coronoids. It is also known as polycyclic conjugated hydrocarbons.
Ali N. A. Koam +3 more
doaj +2 more sources
Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid
Mathematics, 2021 Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids.
Ali N. A. Koam +3 more
doaj +2 more sources
The maximum number of edges in a graph of bounded dimension, with applications to ring theory
Discrete Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Agnarsson, Geir +2 more
openaire +4 more sources
The Mixed Partition Dimension: A New Resolvability Parameter in Graph Theory
IEEE AccessIn this article, we introduce a novel graph-theoretical parameter called the mixed partition dimension and apply it to the path graph and the hexagonal network.
Siti Norziahidayu Amzee Zamri +4 more
doaj +2 more sources
Limit theory of sparse random geometric graphs in high dimensions [PDF]
Stochastic Processes and their Applications, 2023 We study topological and geometric functionals of $l_\infty$-random geometric graphs on the high-dimensional torus in a sparse regime, where the expected number of neighbors decays exponentially in the dimension. More precisely, we establish moment asymptotics, functional central limit theorems and Poisson approximation theorems for certain functionals
Gilles Bonnet +3 more
openaire +2 more sources
A general automatic method for optimal construction of matrix product operators using bipartite graph theory. [PDF]
Journal of Chemical Physics, 2020 Constructing matrix product operators (MPOs) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation.
Jiajun Ren +3 more
semanticscholar +1 more source