Results 41 to 50 of about 77,334 (248)
A Note Concerning Hamilton Cycles in Some Classes of Grid Graphs
Journal of Mathematical and Fundamental Sciences, 2013 A graph G is called hamiltonian if it contains a Hamilton cycle, i.e. a cycle containing all vertices. Deciding whether a given graph has a Hamilton cycle is an NP-complete problem. But, it is a polynomial problem within some special graph classes.
A. N.M. Salman +2 more
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Hierarchical Hexagon: A New Fault-Tolerant Interconnection Network for Parallel Systems
Cybernetics and Information Technologies, 2021 A new interconnection network topology called Hierarchical Hexagon HH(n) is proposed for massively parallel systems. The new network uses a hexagon as the primary building block and grows hierarchically.
Tripathy Laxminath +1 more
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Removable matchings and hamiltonian cycles
Discrete Mathematics, 2009 The authors show the following two results: {\parindent=5mm \begin{itemize}\item[1)]Let \(G\) be a graph of order \(n\geq 4k+3\) with \(\sigma_2 (G)\geq n\) and let \(F\) be a matching of size \(k\) in \(G\) such that \(G-F\) is 2-connected. Then \(G-F\) is hamiltonian or \(G\cong K_2 +(K_2\cup K_{n-4})\) or \(G\cong \bar{K_2} +(K_2\cup K_{n-4 ...
Hu, Zhiquan, Li, Hao
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Hamiltonian paths on Platonic graphs
International Journal of Mathematics and Mathematical Sciences, 2004 We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate
Brian Hopkins
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Energy Conditions for Hamiltonian and Traceable Graphs
Universal Journal of Mathematics and Applications, 2019 A graph is called Hamiltonian (resp. traceable) if the graph has a Hamiltonian cycle (resp. path), a cycle (resp. path) containing all the vertices of the graph. The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the
Rao Li
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Fan's condition on induced subgraphs for circumference and pancyclicity [PDF]
Opuscula Mathematica, 2017 Let \(\mathcal{H}\) be a family of simple graphs and \(k\) be a positive integer. We say that a graph \(G\) of order \(n\geq k\) satisfies Fan's condition with respect to \(\mathcal{H}\) with constant \(k\), if for every induced subgraph \(H\) of \(G ...
Wojciech Wideł
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Strain Engineering of Magnetoresistance and Magnetic Anisotropy in CrSBr
Advanced Materials, EarlyView.Biaxial compressive strain significantly enhances magnetoresistance and critical saturation fields in thin flakes of the 2D magnet CrSBr, along all three crystallographic axes. First‐principles calculations link these effects to strain‐induced increases in exchange interactions and magnetic anisotropy.
Eudomar Henríquez‐Guerra +19 more
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On Uniquely Hamiltonian Claw-Free and Triangle-Free Graphs
Discussiones Mathematicae Graph Theory, 2015 A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. In this note, we prove that claw-free graphs with minimum degree at least 3 are not uniquely Hamiltonian.
Seamone Ben
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A Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs
Discussiones Mathematicae Graph Theory, 2020 Let 𝒫 be a property of a graph. A graph G is said to be locally 𝒫, if the subgraph induced by the open neighbourhood of every vertex in G has property 𝒫. Ryjáček conjectures that every connected, locally connected graph is weakly pancyclic.
Tang Long, Vumar Elkin
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Advanced Materials, EarlyView.AI‐Assisted Workflow for (Scanning) Transmission Electron Microscopy: From Data Analysis Automation to Materials Knowledge Unveiling. Abstract (Scanning) transmission electron microscopy ((S)TEM) has significantly advanced materials science but faces challenges in correlating precise atomic structure information with the functional properties of ...
Marc Botifoll +19 more
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