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On local structures of cubicity 2 graphs
[article]

2016
*
arXiv
*
pre-print

This family

arXiv:1603.09570v1
fatcat:pohuogwanzeqfp4ibparjjhqmi
*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. ...##
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Hydrogen-bond pattern to characterize water network

2019
*
Pure and Applied Chemistry
*

The method is based

doi:10.1515/pac-2018-0721
fatcat:dbmqopkvzbfgnpgje3c2qqkd2y
*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. ...##
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CKConv: Learning Feature Voxelization for Point Cloud Analysis
[article]

2021
*
arXiv
*
pre-print

Despite the remarkable success

arXiv:2107.12655v1
fatcat:ctcdhjn3lnhlbmdw3cd6s63pfi
*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. ...##
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Tutte relations, TQFT, and planarity of cubic graphs
[article]

2015
*
arXiv
*
pre-print

The proofs

arXiv:1512.07339v1
fatcat:2ciouelmjncp5b7gee4ndlbnza
*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*. ...##
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Difficult Instances of the Counting Problem for 2-quantum-SAT are Very Atypical

2014
*
Theory of Quantum Computation, Communication, and Cryptography
*

are states which minimize the energy

doi:10.4230/lipics.tqc.2014.118
dblp:conf/tqc/Beaudrap14
fatcat:cep6zrfv2zgt3jkn64jngu4g6i
*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 ...##
###
Localization of eigenvectors in random graphs

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. ...

##
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Interdimensional optical isospectrality inspired by graph networks

2016
*
Optica
*

This inter-dimensional isospectrality between high- and low-degree

doi:10.1364/optica.3.000836
fatcat:zasjuf3qjzd3dgfebzvphzkmnm
*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*. ...##
###
Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance

2018
*
Physical Review Letters
*

Assuming

doi:10.1103/physrevlett.120.231602
pmid:29932696
fatcat:mrq3kzcf4zfedpl4yg7rrg72jq
*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. ...##
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On the automorphism groups of symmetric graphs admitting an almost simple group

2008
*
European journal of combinatorics (Print)
*

Finally, as

doi:10.1016/j.ejc.2007.06.015
fatcat:bowafjzf5jalta5gk4fr2qnevq
*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] ). ...##
###
Tetrachromagea
[article]

2015
*
arXiv
*
pre-print

We construct a moduli space

arXiv:1505.04487v1
fatcat:son2yv7cdjfercmp4qzxypwmxe
*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. ...##
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On Cayley graphs of {\bb Z}^4

2020
*
Acta Crystallographica Section A: Foundations and Advances
*

Six exceptional, rather 'dense'

doi:10.1107/s2053273320007159
pmid:32869756
pmcid:PMC7459770
fatcat:hqvs37z3lnaktchrgkb46oz6aa
*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. ...##
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Molecular aggregation in liquid water: Laplace spectra and spectral clustering of H-bonded network
[article]

2020
*
arXiv
*
pre-print

These results suggest that six communities are always formed in our simulated systems independently

arXiv:2009.00955v1
fatcat:uwfvasdhsjazjjvlcc6rvzhigm
*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. ...##
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Data complexity measured by principal graphs

2013
*
Computers and Mathematics with Applications
*

We introduce three natural types

doi:10.1016/j.camwa.2012.12.009
fatcat:p7zk33pt4rbc5nyupapc45h52i
*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] . ...##
###
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

2004
*
Physical Review B
*

The

doi:10.1103/physrevb.69.134415
fatcat:en7bjvkgpvfyvnumra2clkwfvy
*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. ...
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