Results 1 to 10 of about 87,555 (181)
Generation of cubic graphs and snarks with large girth [PDF]
Journal of Graph Theory, 2017 We describe two new algorithms for the generation of all non-isomorphic cubic graphs with girth at least $k\ge 5$ which are very efficient for $5\le k \le 7$ and show how these algorithms can be efficiently restricted to generate snarks with girth at ...
Brinkmann, Gunnar, Goedgebeur, Jan
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A comprehensive study on the microstructure and mechanical properties of arc girth welded joints of spiral welded high strength API X70 steel pipe [PDF]
Archives of Civil and Mechanical Engineering, 2020 In the paper, the effect of welding technology on the microstructure and mechanical properties of girth welded joints was presented. Metallographic examinations based on light microscopy and SEM were conducted on girth welded joints of API X70 steel pipe.
De Waele, Wim +6 more
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Ars Mathematica Contemporanea, 17(2):349--368, 2019, 2018 We introduce a notion of a girth-regular graph as a $k$-regular graph for which there exists a non-descending sequence $(a_1, a_2, \dots, a_k)$ (called the signature) giving, for every vertex $u$ of the graph, the number of girth cycles the edges with end-vertex $u$ lie on.
P. Potočnik, Janoš Vidali
arxiv +3 more sources
High-Girth Matrices and Polarization [PDF]
arXiv, 2015 The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of {\it high-girth} matrices, whose probabilistic girth is
Abbe, Emmanuel, Wigderson, Yuval
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Constructing Large Girth QC Protograph LDPC Codes Based on PSD-PEG Algorithm
IEEE Access, 2017 For a given base graph, the lifted graph can be obtained by a copy-and-permute procedure. If the permutation is cyclic, the lifted graph corresponds to a quasi-cyclic (QC) protograph low-density parity-check (LDPC) code.
Xue-Qin Jiang +3 more
doaj +2 more sources
Computing Graph Roots Without Short Cycles [PDF]
26th International Symposium on Theoretical Aspects of Computer
Science STACS 2009 (2009) 397-408, 2009 Graph G is the square of graph H if two vertices x, y have an edge in G if and only if x, y are of distance at most two in H. Given H it is easy to compute its square H2, however Motwani and Sudan proved that it is NP-complete to determine if a given ...
Farzad, Babak +3 more
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Tanner
IEEE Access, 2019 Girth plays an important role in the design of low-density parity-check (LDPC) codes. Motivated by the works on the girth of some classes of Tanner quasi-cyclic (QC) LDPC codes, e.g., Tanner (3, 5), (3, 7), (3, 11), and (5, 7) codes, we, in this paper ...
Hengzhou Xu +4 more
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Bounds for the Zero Forcing Number of Graphs with Large Girth [PDF]
Theory and Applications of Graphs, 2015 The zero-forcing number, Z(G) is an upper bound for the maximum nullity of all symmetric matrices with a sparsity pattern described by the graph. A simple lower bound is δ ≤ Z(G) where δ is the minimum degree.
Randy Davila, Franklin Kenter
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The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model [PDF]
Theory of Quantum Computation, Communication, and Cryptography, 2021 The Quantum Approximate Optimization Algorithm (QAOA) finds approximate solutions to combinatorial optimization problems. Its performance monotonically improves with its depth $p$. We apply the QAOA to MaxCut on large-girth $D$-regular graphs. We give an
J. Basso +4 more
semanticscholar +1 more source
Classical algorithms and quantum limitations for maximum cut on high-girth graphs [PDF]
Information Technology Convergence and Services, 2021 We study the performance of local quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) for the maximum cut problem, and their relationship to that of classical algorithms.
B. Barak, Kunal Marwaha
semanticscholar +1 more source