Results 61 to 70 of about 34,294 (314)
On new results on extremal graph theory, theory of algebraic graphs, and their applications
Reports of the National Academy of Sciences of Ukraine, 2022 New explicit constructions of infinite families of finite small world graphs of large girth with well-defined projective limits which is an infinite tree are described. The applications of these objects to constructions of LDPC codes and cryptographic algorithms are shortly observed.
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Compactness results in extremal graph theory [PDF]
Combinatorica, 1982 (From the authors' abstract:) ``Let \(L\) be a given family of \dots 'prohibited graphs'. Let \(\text{ex}(n,L)\) denote the maximum number of edges a simple graph of order n can have without containing subgraphs from \(L\). A typical extremal graph problem is to determine \(\text{ex}(n,L)\), or, at least, to find good bounds on it.
Erdős, Paul, Simonovits, M.
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Advanced Functional Materials, EarlyView.A lack of standard approaches for testing and reporting the performance of metal halide perovskites and organic semiconductor radiation detectors has resulted in inconsistent interpretation of performance parameters, impeding progress in the field. This Perspective recommends key metrics and experimental details, which are suggested for reporting in ...
Jessie A. Posar +8 more
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Vojnotehnički GlasnikIntroduction/purpose: Degree-based graph invariants are a type of molecular descriptor that represent the connectivity of atoms (vertices) in a molecule through bonds (edges). They are used to model structural properties of molecules and provide valuable
Ochirbat Altangoo +3 more
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Edge-Removal and Non-Crossing Configurations in Geometric Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2010 Graphs and ...
Oswin Aichholzer +7 more
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On Bond Incident Degree Indices of Chemical Graphs
Mathematics, 2022 By swapping out atoms for vertices and bonds for edges, a graph may be used to model any molecular structure. A graph G is considered to be a chemical graph in graph theory if no vertex of G has a degree of 5 or greater.
Abeer M. Albalahi +6 more
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Advanced Functional Materials, EarlyView.AI is transforming the research paradigm of battery materials and reshaping the entire landscape of battery technology. This comprehensive review summarizes the cutting‐edge applications of AI in the advancement of battery materials, underscores the critical challenges faced in harnessing the full potential of AI, and proposes strategic guidance for ...
Qingyun Hu +5 more
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Breaking Symmetries in Graph Representation [PDF]
, 2013 There are many complex combinatorial problems which involve searching for an undirected graph satisfying a certain property. These problems are often highly challenging because of the large number of isomorphic representations of a possible solution.
Codish, M. +3 more
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Advanced Functional Materials, EarlyView.This study introduces a novel multi‐scale scaffold design using L‐fractals arranged in Archimedean tessellations for tissue regeneration. Despite similar porosity, tiles display vastly different tensile responses (1–100 MPa) and deformation modes. In vitro experiments with hMSCs show geometry‐dependent growth and activity. Over 55 000 tile combinations
Maria Kalogeropoulou +4 more
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On singular probability densities generated by extremal dynamics
, 2004 Extremal dynamics is the mechanism that drives the Bak-Sneppen model into a (self-organized) critical state, marked by a singular stationary probability density $p(x)$.
Bak +23 more
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