Results 41 to 50 of about 952,320 (325)

Graph fractal dimension and the structure of fractal networks

J. Complex Networks, 2020
Fractals are geometric objects that are self-similar at different scales and whose geometric dimensions differ from so-called fractal dimensions. Fractals describe complex continuous structures in nature.
P. Skums, L. Bunimovich
semanticscholar   +1 more source

The spectral dimension of simplicial complexes: a renormalization group theory [PDF]

Journal of Statistical Mechanics: Theory and Experiment, 2019
Simplicial complexes are increasingly used to study complex system structures and dynamics including diffusion, synchronization and epidemic spreading. The spectral dimension of the graph Laplacian is known to determine the diffusion properties at long ...
G. Bianconi, S. Dorogovtsev
semanticscholar   +1 more source

THE GRAPH-REPRESENTATION APPROACH TO TOPOLOGICAL FIELD THEORY IN 2 + 1 DIMENSIONS [PDF]

International Journal of Modern Physics A, 1992
An alternative definition of topological quantum field theory in 2 + 1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but nonlocal observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of
openaire   +6 more sources

On the Partition Dimension of Tri-Hexagonal α-Boron Nanotube

IEEE Access, 2021
The production of low-cost, small in size, and high in efficiency objects is the topic of research in almost all scientific fields, especially of engineering. In this scenario, nanotechnology becomes of great importance. To achieve these tasks, one needs
Ayesha Shabbir, Muhammad Azeem
semanticscholar   +1 more source

Asymptotic Dimension of Minor-Closed Families and Assouad-Nagata Dimension of Surfaces [PDF]

Journal of the European Mathematical Society (Print), 2020
The asymptotic dimension is an invariant of metric spaces introduced by Gromov in the context of geometric group theory. In this paper, we study the asymptotic dimension of metric spaces generated by graphs and their shortest path metric and show their ...
Marthe Bonamy, N. Bousquet, Louis Esperet, Carla Groenland, Chun-Hung Liu, F. Pirot, A. Scott   +6 more
semanticscholar   +1 more source

A Comparative Study of Three Resolving Parameters of Graphs

Complexity, 2021
Graph theory is one of those subjects that is a vital part of the digital world. It is used to monitor the movement of robots on a network, to debug computer networks, to develop algorithms, and to analyze the structural properties of chemical structures,
Hafiz Muhammad Ikhlaq, Hafiz Muhammad Afzal Siddiqui, Muhammad Imran   +2 more
doaj   +1 more source

Topological Graph Polynomials in Colored Group Field Theory [PDF]

, 2009
In this paper we analyze the open Feynman graphs of the Colored Group Field Theory introduced in [arXiv:0907.2582]. We define the boundary graph $\cG_{\partial}$ of an open graph $\cG$ and prove it is a cellular complex.
A. Connes, B. Bollobás, B. Bollobás, B. Bollobás, C. Itzykson, D. Boulatov, E.R. Livine, F. Conrady, F. David, G. Kirchhoff, G. ‘t Hooft, G. ’t Hooft, H. Grosse, H. Grosse, H. Grosse, H.H. Crapo, J. Engle, J. Engle, J.B. Geloun, L. Freidel, L. Freidel, L. Freidel, M. Disertori, M. Disertori, M. Gross, M.R. Douglas, N. Nakanishi, N. Sasakura, R. De Pietri, R. Gurau, R. Gurau, R. Gurau, R. Gurau, Razvan Gurau, V. Bonzom, V. Rivasseau, V. Rivasseau, W.T. Tutte   +37 more
core   +1 more source

Computing the Metric Dimension of a Graph from Primary Subgraphs [PDF]

Discussiones Mathematicae Graph Theory, 2013
Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . .
D. Kuziak, J. A. Rodríguez-Velázquez, I. G. Yero   +2 more
semanticscholar   +1 more source

The partition dimension of a subdivision of a homogeneous firecracker

Electronic Journal of Graph Theory and Applications, 2020
Finding the partition dimension of a graph is one of the interesting (and uncompletely solved) problems of graph theory. For instance, the values of the partition dimensions for most kind of trees are still unknown.  Although for several classes of trees
Amrullah Amrullah
doaj   +1 more source

Dimension and cut vertices: an application of Ramsey theory [PDF]

arXiv.org, 2015
Motivated by quite recent research involving the relationship between the dimension of a poset and graph-theoretic properties of its cover graph, we show that for every $d\geq 1$, if $P$ is a poset and the dimension of a subposet $B$ of $P$ is at most $d$
W. T. Trotter, Bartosz Walczak, Ruidong Wang   +2 more
semanticscholar   +1 more source