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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
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Dimension theory of graphs and networks [PDF]
Journal of Physics A: Mathematical and General, 1998 Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the discrete protoforms of the building blocks of continuum physics and mathematics.
Nowotny, Thomas, Requardt, Manfred
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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
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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
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Dimension Theory of Some Non-Markovian Repellers Part II: Dynamically Defined Function Graphs [PDF]
, 2021 This is the second part in a series of two papers. Here, we give an overview on the dimension theory of some dynamically defined function graphs, like Takagi and Weierstrass function, and we study the dimension of Markovian fractal interpolation functions and generalised Takagi functions generated by non-Markovian dynamics.
Bárány, Balázs +2 more
+6 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
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Extremal Graph Theory for Metric Dimension and Girth [PDF]
, 2012 6 ...
Mohsen Jannesari
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The d=6 trace anomaly from quantum field theory four-loop graphs in one dimension [PDF]
Nuclear Physics B, 2001 23 pages, 17 ...
Hatzinikitas, A., Portugal, R.
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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
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, 2019 The Weisfeiler-Leman (WL) dimension of a graph is a measure for the inherent descriptive complexity of the graph. While originally derived from a combinatorial graph isomorphism test called the Weisfeiler-Leman algorithm, the WL dimension can also be characterised in terms of the number of variables that is required to describe the graph up to ...
Grohe, Martin, Kiefer, Sandra
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