Results 41 to 50 of about 77,685 (270)
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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A Survey on Hamiltonian Cycles
Interdisciplinary Information Sciences, 2001 The author surveys some of the classical results on Hamiltonian cycles in undirected graphs and pays particular attention to the development over the last decade. Among the subjects are: binding number, toughness, degree conditions, closure, regular graphs, and graphs on surfaces. This is intended as a supplement to the survey of \textit{R. J.
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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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Polarizable Vanadium Dipoles Promote Water Dissociation on Vanadium‐Based Metal Organic Framework
Advanced Functional Materials, EarlyView.The polarization of unpaired V 3d electrons weakens the H─O bond to improve water dissociation by the dual Vδ+:O─H and Pλ−:H─O coupling hydrogen bonds formation and relaxation. P@V‐MOF electrocatalyst shows low overpotentials (94 mV in acid, 178 mV in neutral, and 77 mV in alkaline solutions) with excellent stability for effective overall water ...
Xinjuan Liu +13 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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Hamiltonian chordal graphs are not cycle extendible [PDF]
, 2014 In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle extendible; that is, the vertices of any non-Hamiltonian cycle are contained in a cycle of length one greater.
Lafond, Manuel, Seamone, Ben
core
Hamiltonian Cycles in the Square of a Graph [PDF]
The Electronic Journal of Combinatorics, 2011 We show that under certain conditions the square of the graph obtained by identifying a vertex in two graphs with hamiltonian square is also hamiltonian. Using this result, we prove necessary and sufficient conditions for hamiltonicity of the square of a connected graph such that every vertex of degree at least three in a block graph corresponds to a
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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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