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Extremal Graph Theory for Metric Dimension and Diameter [PDF]
Electronic Notes in Discrete Mathematics, 2007 A set of vertices $S$ \emph{resolves} a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of $G$ is the minimum cardinality of a resolving set of $G$. Let $\mathcal{G}
Carmen Hernando +4 more
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Extremal Graph Theory for Metric Dimension and Diameter [PDF]
Electronic Journal of Combinatorics, 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 $G$.
Carmen Hernando +4 more
semanticscholar +5 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 Introduction: Graph theoretical analysis of functional Magnetic Resonance Imaging (fMRI) data has provided new measures of mapping human brain in vivo.
Meysam Siyah Mansoory +3 more
semanticscholar +6 more sources
The maximum number of edges in a graph of bounded dimension, with applications to ring theory [PDF]
Discrete Mathematics, 1999 AbstractWith a finite graph G = (V, E), we associate a partially ordered set P = (X, P) with X = V ∪ E and x < e in P if and only if x is an endpoint of e in G. This poset is called the incidence poset of G. In this paper, we consider the function M(p, d) defined for p, d ⩾ 2 as the maximum number of edges a graph G can have when it has p vertices and ...
Geir Agnarsson +2 more
semanticscholar +5 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 +3 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
The d=6 trace anomaly from quantum field theory four-loop graphs in one dimension [PDF]
Nuclear Physics B, 2001 23 pages, 17 ...
Agapitos Hatzinikitas, Renato Portugal
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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.
Thomas Nowotny, Manfred Requardt
openalex +5 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.
W. Kandasamy +2 more
semanticscholar +3 more sources