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On local structures of cubicity 2 graphs [article]

Sujoy Kumar Bhore, Dibyayan Chakraborty, Sandip Das, Sagnik Sen
2016 arXiv   pre-print
This family of graphs allow us to study local structures of unit square intersection graphs, that is, graphs with cubicity 2.  ...  The complexity of determining whether a tree has cubicity 2 is unknown while the graph recognition problem for unit square intersection graph is known to be NP-hard.  ...  In a recent work [2] , some new families of graphs, based on the local structure of boxicity 2 and cubicity 2 graphs were introduced and studied.  ... 
arXiv:1603.09570v1 fatcat:pohuogwanzeqfp4ibparjjhqmi

Hydrogen-bond pattern to characterize water network

Misako Aida, Dai Akase
2019 Pure and Applied Chemistry  
The method is based on the combination of molecular simulation with graph theory.  ...  At a finite temperature it can be observed that other isomers than local minimum structures on the potential energy surface are highly populated.  ...  Acknowledgment: This mini-review is based on the research which has been performed at the Quantum Chemistry Research Group of Hiroshima University.  ... 
doi:10.1515/pac-2018-0721 fatcat:dbmqopkvzbfgnpgje3c2qqkd2y

CKConv: Learning Feature Voxelization for Point Cloud Analysis [article]

Sungmin Woo, Dogyoon Lee, Junhyeop Lee, Sangwon Hwang, Woojin Kim, Sangyoun Lee
2021 arXiv   pre-print
Despite the remarkable success of deep learning, optimal convolution operation on point cloud remains indefinite due to its irregular data structure.  ...  In this paper, we present Cubic Kernel Convolution (CKConv) that learns to voxelize the features of local points by exploiting both continuous and discrete convolutions.  ...  Figure 2 . 2 Overall CKConv process on a local point set with number of neighboring points N = 3 and kernel unit size v = 3.  ... 
arXiv:2107.12655v1 fatcat:ctcdhjn3lnhlbmdw3cd6s63pfi

Tutte relations, TQFT, and planarity of cubic graphs [article]

Ian Agol, Vyacheslav Krushkal
2015 arXiv   pre-print
The proofs of these results rely on the structure of the Temperley-Lieb algebra and more generally on methods of topological quantum field theory.  ...  A version of the Tutte linear relation for the flow polynomial at (3-√(5))/2 is shown to give a planarity criterion for 3-connected cubic graphs.  ...  However the graph denoted H 2 in the figure depends on a choice of a ribbon structure near the edge e. There are two such choices, figure 7. e Two ribbon structures near an edge of a cubic graph.  ... 
arXiv:1512.07339v1 fatcat:2ciouelmjncp5b7gee4ndlbnza

Difficult Instances of the Counting Problem for 2-quantum-SAT are Very Atypical

Niel De Beaudrap, Marc Herbstritt
2014 Theory of Quantum Computation, Communication, and Cryptography  
are states which minimize the energy of each interaction term ground states more eaily locally verified :-)  ...  Frustrated Hamiltonian: one for which there aren't states which minimize the energy of each interaction term more difficult to study the ground states Frustration-free Hamiltonian: one for which there  ...  models 3 Summary models of random graphs (part 2) More physically motivated: Hamiltonians defined on a spin lattice (e.g. square/cubic grids) We consider edge-percolated square/cubic lattice models for  ... 
doi:10.4230/lipics.tqc.2014.118 dblp:conf/tqc/Beaudrap14 fatcat:cep6zrfv2zgt3jkn64jngu4g6i

Localization of eigenvectors in random graphs

F. Slanina
2012 European Physical Journal B : Condensed Matter Physics  
On the contrary, on cubic graphs the fraction of localized states is large and tends to 1 when the strength of the disorder increases, implying that for sufficiently strong disorder all states are localized  ...  The first class comprises the adjacency matrices of Erdos-Renyi (ER) random graphs. The second one corresponds to random cubic graphs, with Gaussian random variables on the diagonal.  ...  This work was carried out within the project AV0Z10100520 of the Academy of Sciences of the Czech Republic and was supported by the MŠMT of the Czech Republic, grant no. OC09078.  ... 
doi:10.1140/epjb/e2012-30338-1 fatcat:usq6pqjypvg2jh3hmjc5nua7py

Interdimensional optical isospectrality inspired by graph networks

Sunkyu Yu, Xianji Piao, Jiho Hong, Namkyoo Park
2016 Optica  
This inter-dimensional isospectrality between high- and low-degree graph-like structures enables the ultimate simplification of broadband multilevel devices, from three- to one-dimensional structures.  ...  Utilizing discretization schemes, both electrical and optical materials can also be interpreted as abstract 'graph' networks composed of couplings (edges) between local elements (vertices), which define  ...  (a) A cubic lattice and (b) its randomly deformed structure.  ... 
doi:10.1364/optica.3.000836 fatcat:zasjuf3qjzd3dgfebzvphzkmnm

Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance

Nima Arkani-Hamed, Laurentiu Rodina, Jaroslav Trnka
2018 Physical Review Letters  
Assuming locality (that the singularities are associated with the poles of cubic graphs), we prove that gauge-invariance in just (n-1) particles together with minimal power-counting uniquely fixes the  ...  power-counting demand a graph structure for singularities.  ...  For each cubic graph Γ, we get D ðΓÞ n ¼ N ðΓÞ n ðϵ i ; p j Þ P 2 σ 1 P 2 σ 2 …P 2 σ n−3 ; ð3Þ where all the factors P 2 σ a in the denominator come from Feynman propagators of cubic diagrams.  ... 
doi:10.1103/physrevlett.120.231602 pmid:29932696 fatcat:mrq3kzcf4zfedpl4yg7rrg72jq

On the automorphism groups of symmetric graphs admitting an almost simple group

Xin Gui Fang, Lu Jun Jia, Jie Wang
2008 European journal of combinatorics (Print)  
Finally, as one of the applications of our results, we determine the structure of the automorphism group Aut Γ for cubic symmetric graph Γ admitting a finite almost simple group.  ...  Then we describe the structure of the full automorphism group of G-locally primitive graphs of valency d, where d ≤ 20 or is a prime.  ...  The first lemma gives a general description of structures of the point stabilizer of connected cubic symmetric graphs. Lemma 2.1 ( [1, 11] ).  ... 
doi:10.1016/j.ejc.2007.06.015 fatcat:bowafjzf5jalta5gk4fr2qnevq

Tetrachromagea [article]

Jimmy Dillies
2015 arXiv   pre-print
We construct a moduli space of four colorings on planar cubic graphs.  ...  Weak Hamiltonians have a form of deformation, which we call mutation, which gives them a graph structure, the Weak Hamiltonian graph. This graph encodes the different colorings as 3 vertex cliques.  ...  Mutations endow the set of weak Hamiltonians of a graph structure (the weak Hamiltonian graph, d) and, hereby, the set of colorings of a graph structure, the chromatic graph χ.  ... 
arXiv:1505.04487v1 fatcat:son2yv7cdjfercmp4qzxypwmxe

On Cayley graphs of {\bb Z}^4

Igor A. Baburin
2020 Acta Crystallographica Section A: Foundations and Advances  
Six exceptional, rather 'dense' graphs have been identified which are locally isomorphic to a five-dimensional cubic lattice within a ball of radius 10.  ...  To compute automorphism groups, a novel strategy is introduced that is based on determining vertex stabilizers from the automorphism group of a sufficiently large finite ball cut out from an infinite graph  ...  Here we have adopted a different strategy that involves a computation of a vertex stabilizer in Aut(À) from the local structure of a graph À.  ... 
doi:10.1107/s2053273320007159 pmid:32869756 pmcid:PMC7459770 fatcat:hqvs37z3lnaktchrgkb46oz6aa

Molecular aggregation in liquid water: Laplace spectra and spectral clustering of H-bonded network [article]

Imre Bakó, Dániel Csókás, Szilvia Pothoczki
2020 arXiv   pre-print
These results suggest that six communities are always formed in our simulated systems independently of the number of molecules in the cubic box.  ...  Application of the spectral clustering method based on the analyses of the Laplace matrix is an acceptable indicator of the global properties of H-bonded network.  ...  Pothoczki acknowledges that this project was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.  ... 
arXiv:2009.00955v1 fatcat:uwfvasdhsjazjjvlcc6rvzhigm

Data complexity measured by principal graphs

Andrei Zinovyev, Evgeny Mirkes
2013 Computers and Mathematics with Applications  
We introduce three natural types of data complexity: 1) geometric (deviation of the data's approximator from some "idealized" configuration, such as deviation from harmonicity); 2) structural (how many  ...  The type of the principal cubic complex is determined by its dimension and a grammar of elementary graph transformations. The simplest grammar produces principal trees.  ...  In simple words, principal cubic complex is a Cartesian product of graphs ( Fig. 1) . One-dimensional principal cubic complex is simply a principal graph [10] .  ... 
doi:10.1016/j.camwa.2012.12.009 fatcat:p7zk33pt4rbc5nyupapc45h52i

Page 8493 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
Further results toward this end include the following, where k > 3: a connected locally (G,2s)- arc transitive graph of valency {2,k} is locally (G,2s + 1)-are transitive; the connected locally (G,2s —  ...  is the Gray graph on 54 vertices. The authors show in the main result of this paper that the Gray graph is, in fact, the only cubic semi- symmetric graph of order 2p*, p a prime.  ... 

Electronic structure and ferromagnetism in the martensitic-transformation materialNi2FeGa

Z. H. Liu, H. N. Hu, G. D. Liu, Y. T. Cui, M. Zhang, J. L. Chen, G. H. Wu, Gang Xiao
2004 Physical Review B  
The localized moment of Fe atom is interpreted based on the electronic structure and the popular explanation of the localized moment of Mn in Heusler alloy X 2 MnY .  ...  Comparing the density of states of cubic and orthorhombic structures, we observed that a Ni peak near the density of states of d band for the cubic structure splits for the orthorhombic structure, indicating  ...  The authors would like to appreciate Professor Dingsheng Wang for his helpful discussion on the electronic structure calculation.  ... 
doi:10.1103/physrevb.69.134415 fatcat:en7bjvkgpvfyvnumra2clkwfvy
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