Results 1 to 10 of about 28,886 (232)
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 $D$.
C Hernando, Mercè Mora, I M Pelayo
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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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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.
Geir Agnarsson +2 more
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Computing Basis and Dimension of Chloroquine and Hydroxychloroquine by Using Chemical Graph Theory
Polycyclic Aromatic Compounds, 2022 Discovering a vaccine with reliable and effective treatment for the new corona virus disease 2019 (COVID-19) is indeed a long way off, and there seems to be a critical need to research additional viable medications that could save countless lives in the ...
Yogesh Singh +3 more
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Extremal graph theory for metric dimension and diameter [PDF]
, 2010 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 G ,D be the set of graphs with metric dimension and diameter D.
Hernando Martín, María del Carmen +3 more
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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. This parameter builds on the concept of resolvability in graphs, integrating vertex-based partition dimensions with edge-oriented strategies to characterize the complexity of graph structures ...
Sikander Ali +2 more
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Discrete Mathematics, 2010 In the invited chapter Discrete Spatial Models of the book Handbook of Spatial Logics, we have introduced the concept of dimension for graphs, which is inspired by Evako’s idea of dimension of graphs [A.V. Evako, R. Kopperman, Y.V.
Michael B Smyth, Iain Stewart
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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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Limit theory of sparse random geometric graphs in high dimensions
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
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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
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