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Computation of mixed resolvability for a circular ladder and its unbounded nature. [PDF]
PLoS ONELet Γ = Γ(V ,E) be a simple, planar, connected, and undirected graph. The article primarily concentrates on a category of planar graphs, detailing the explicit identification of each member within this graph family. Within the domain of graph theory, the
Sunny Kumar Sharma +4 more
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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
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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
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Dimension Theory of some non-Markovian repellers Part II: Dynamically defined function graphs [PDF]
, 2019 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.
Balázs Bárány +2 more
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Exploring metric dimension of nanosheets, nanotubes, and nanotori of SiO2. [PDF]
PLoS ONEThis work investigates the metric dimension (MD) and edge metric dimension (EMD) of SiO2 nanostructures, specifically nanosheets, nanotubes, and nanotorii.
Umar Farooq +4 more
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Edge length dynamics on graphs with applications to p-adic AdS/CFT [PDF]
Journal of High Energy Physics, 2017 We formulate a Euclidean theory of edge length dynamics based on a notion of Ricci curvature on graphs with variable edge lengths. In order to write an explicit form for the discrete analog of the Einstein-Hilbert action, we require that the graph should
Steven S. Gubser +7 more
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Journal of Mathematics ResearchUrban transportation networks play a crucial role in modern city planning, requiring efficient design, optimization, and management strategies. This study examines the Lahore Metro Orange Line using a combination of graph theory and multi-criteria decision-making (MCDM) techniques, specifically the metric dimension analysis, VIKOR, and PROMETHEE ...
Umar Farooq +2 more
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Modular graph functions and odd cuspidal functions. Fourier and Poincaré series [PDF]
Journal of High Energy Physics, 2019 Modular graph functions are SL(2, ℤ)-invariant functions associated with Feynman graphs of a two-dimensional conformal field theory on a torus of modulus τ. For one-loop graphs they reduce to real analytic Eisenstein series. We obtain the Fourier series,
Eric D’Hoker, Justin Kaidi
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Graph Theory Solution Method to Solve The Complex Assembly Dimension Chain [PDF]
Advances in Computer Science Research, 2017 Ya Zhang, Zhang Li
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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
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