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Fundamental Groupoids for Graphs [PDF]
Categories and General Algebraic Structures with Applications, 2022 In recent years several notions of discrete homotopy for graphs have been introduced, including a notion of ×-homotopy due to Dochtermann. In this paper, we define a ×-homotopy fundamental groupoid for graphs, and prove that it is a functorial ×-homotopy
Tien Chih, Laura Scull
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Spatio–Spectral Limiting on Replacements of Tori by Cubes
Mathematics, 2023 A class of graphs is defined in which each vertex of a discrete torus is replaced by a Boolean hypercube in such a way that vertices in a fixed subset of each replacement cube are adjacent to corresponding vertices of a neighboring replacement cube ...
Jeffrey A. Hogan, Joseph D. Lakey
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Моделирование и анализ информационных систем, 2021 Modern network systems (unmanned aerial vehicles groups, social networks, network production chains, transport and logistics networks, communication networks, cryptocurrency networks) are distinguished by their multi-element nature and the dynamics of ...
Aleksandr Vasil'evich Tymoshenko +2 more
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Not all planar graphs are in PURE-4-DIR
Journal of Graph Algorithms and Applications, 2020 We prove that some planar graphs are not intersection graphs of segments if only four slopes are allowed for the segments, and if parallel segments do not intersect. This refutes a conjecture of D. West [D. West, SIAM J. Discrete Math. Newsletter, 1991].
Daniel Gonçalves
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Discrete Random Walks on One-Sided ``Periodic'' Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 In this paper we consider discrete random walks on infinite graphs that are generated by copying and shifting one finite (strongly connected) graph into one direction and connecting successive copies always in the same way.
Michael Drmota
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Discrete Integral and Discrete Derivative on Graphs and Switch Problem of Trees
Mathematics, 2023 For a vertex and edge weighted (VEW) graph G with a vertex weight function fG let Wα,β(G)=∑{u,v}⊆V(G)[αfG(u)×fG(v)+β(fG(u)+fG(v))]dG(u,v) where, α,β∈ℝ and dG(u,v) denotes the distance, the minimum sum of edge weights across all the paths connecting u,v∈V(
M. H. Khalifeh, Abdol-Hossein Esfahanian
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On the Inverse Symmetric Division Deg Index of Unicyclic Graphs
Computation, 2022 The symmetric division deg (SDD) index is among the 148 discrete Adriatic indices that were developed about a decade ago. Motivated by the success of the SDD index, Ghorbani et al.
Abeer M. Albalahi, Akbar Ali
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Cryptanalysing the critical group: efficiently solving Biggs's discrete logarithm problem
Journal of Mathematical Cryptology, 2009 Biggs has recently proposed the critical group of a certain class of finite graphs as a platform group for cryptosystems relying on the difficulty of the discrete log problem. The paper uses techniques from the theory of Picard groups on finite graphs to
Blackburn Simon R.
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Crossing Numbers of Join Product with Discrete Graphs: A Study on 6-Vertex Graphs
Mathematics, 2023 Reducing the number of crossings on graph edges can be useful in various applications, including network visualization, circuit design, graph theory, cartography or social choice theory.
Jana Fortes, Michal Staš
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Remarks on Dynamic Monopolies with Given Average Thresholds
Discussiones Mathematicae Graph Theory, 2015 Dynamic monopolies in graphs have been studied as a model for spreading processes within networks. Together with their dual notion, the generalized degenerate sets, they form the immediate generalization of the classical notions of vertex covers and ...
Centeno Carmen C., Rautenbach Dieter
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