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On the spectral Ádám property for circulant graphs

2002
*
Discrete Mathematics
*

We investigate a certain condition

doi:10.1016/s0012-365x(01)00374-0
fatcat:miyhjgzhtzbvjirfxtyaeb2qzu
*for*isomorphism between*circulant**graphs*(known as*the*à Adà am*property*) in a stronger form by referring to isospectrality rather than to isomorphism of*graphs*. ... We apply these results to establish an asymptotic formula*for**the*number of non-isomorphic*circulant**graphs*and connected*circulant**graphs*. ... Acknowledgements We would like to thank Cai Heng Li*for*his comments*on*our original paper and*for*pointing out*the*reference to [12] . ...##
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On the Ádám Conjecture on Circulant Graphs
[chapter]

1998
*
Lecture Notes in Computer Science
*

We investigate

doi:10.1007/3-540-68535-9_29
fatcat:7dmt5mjqv5f4dhsz2g6l5rceou
*the*condition*for*isomorphism between*circulant**graphs*which is known as theÁdám*property*. ... Our method is based*on*studying*the**graph*spectra with*the*aid of some deep results of algebraic number theory. ...*graphs*), has*the**spectraĺ**Adám**property*, provided that 2 ≤ d < min{n/4, ϕ(n)/2}, where ϕ(n) is*the*Euler function. ...##
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Page 4031 of Mathematical Reviews Vol. , Issue 2003f
[page]

2003
*
Mathematical Reviews
*

) ;
Pappalardi, Francesco (I-ROME3; Rome);
Shparlinski, Igor (5-MCQR-CP; North Ryde)

*On**the**spectral**Adam**property**for**circulant**graphs*. ... Asymptotic formulae are obtained, depending*on*n and m,*for**the*number of*circulant*digraphs and, among these,*for**the*number of connected*ones*(up to isomorphism). ...##
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Page 4779 of Mathematical Reviews Vol. , Issue 98H
[page]

1998
*
Mathematical Reviews
*

E.| (1L-BILN-C; Ramat Gan

*On*Adam’s conjecture*for**circulant**graphs*. ... E.| (1L-BILN-CS; Ramat Gan*On*Adam’s conjecture*for**circulant**graphs*. ...##
###
Page 43 of Mathematical Reviews Vol. , Issue 94a
[page]

1994
*
Mathematical Reviews
*

*property*and automorphism groups of directed

*circulant*

*graphs*. ... Let h(G) = logr(G) be

*the*entropy of a directed

*graph*G, where r(G) is

*the*

*spectral*radius of G (see an article by M. Fujii, H. Sasaoka and Y. Watatani [Math. ...

##
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Equivalence of sparse circulants: the bipartite Ádám problem
[article]

2007
*
arXiv
*
pre-print

We also explain how our problem relates to

arXiv:0706.1567v1
fatcat:2dtoegn4p5e6padmoct7zxqvbu
*the**Adam*problem*on*isomorphisms of*circulant*directed*graphs*. ... We give examples showing this result is not always true*for*denser*circulants*, as well as results showing it continues to hold in some situations. ... Our problem asks*the*same question*for*directed bipartite*graphs*which have*the*same group acting*on*each part. ...##
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Spectrum of some arrow-bordered circulant matrix
[article]

2019
*
arXiv
*
pre-print

We find its eigenpairs and we discuss its spectrum with stress

arXiv:1905.04807v1
fatcat:oomn7ukubrcnlnhvsoiyjxakqe
*on*extreme eigenvalues and their bounds. At last we notice its relation to a weighted wheel*graph*... Given a*circulant*matrix circ(c,a,0,0,...,0,a), a 0, of order n, we "border" it from left and from above by constant column and row, respectively, and we set*the*left top entry to be -nc. ...*The*other eigenvalues have no clear physical meaning, nevertheless*properties*of*the*whole spectrum are discussed below. There is an extensive literature*on**spectral**graph*theory. ...##
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Learning Algebraic Multigrid Using Graph Neural Networks
[article]

2020
*
arXiv
*
pre-print

Efficient numerical solvers

arXiv:2003.05744v2
fatcat:2pdfjvtggvga3dwoa3dgo226ye
*for*sparse linear systems are crucial in science and engineering.*One*of*the*fastest methods*for*solving large-scale sparse linear systems is algebraic multigrid (AMG). ... Experiments*on*a broad class of problems demonstrate improved convergence rates compared to classical AMG, demonstrating*the*potential utility of neural networks*for*developing sparse system solvers. ... Acknowledgment This research was supported by*the*Israel Science Foundation, grant No. 1639/19. ...##
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Improving Expressivity of Graph Neural Networks
[article]

2020
*
arXiv
*
pre-print

We propose a

arXiv:2004.05994v1
fatcat:3mqnv7zlgbdqbe3ttqgl4mpsru
*Graph*Neural Network with greater expressive power than commonly used GNNs - not constrained to only differentiate between*graphs*that Weisfeiler-Lehman test recognizes to be non-isomorphic ... We also use partially random initial embeddings, allowing differentiation between nodes that would otherwise look*the*same. ... ACKNOWLEDGEMENT This research was supported by*the*ERC starting grant no. 714034 SMART. ...##
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Page 6 of Mathematical Reviews Vol. , Issue 95a
[page]

1995
*
Mathematical Reviews
*

,

*On**the*monotonicity of*the*diameter of a family of*graphs*(71-82); Charles B. ... Svistula,*On**the*Darboux*property*of a nonadditive set function (Russian) (199-203). ...##
###
A fast time domain solver for the equilibrium Dyson equation
[article]

2021
*
arXiv
*
pre-print

We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations,

arXiv:2110.06120v1
fatcat:utb7i4lo2jf2tapwnhibxkky64
*for*which*the*kernel depends self-consistently*on**the*solution. ... We demonstrate*the*solver with two standard model systems:*the*Bethe*graph*, and*the*Sachdev-Ye-Kitaev model. ... Acknowledgements We thank Alex Barnett*for*helpful discussions. H.U.R.S. acknowledges financial support from*the*ERC synergy grant (854843-FASTCORR). ...##
###
Master index of volumes 221-230

2001
*
Discrete Mathematics
*

Yebra, Boundary

doi:10.1016/s0012-365x(01)00058-9
fatcat:xoeto3fhfra5dhyjrww2tymguu
*graphs*:*The*limit case of a*spectral**property*226 (2001) 155}173 Fleischner, H., (Some of )*the*many uses of Eulerian)*graphs*in*graph*theory (plus some applications) 230 (2001) ... Shen, Diameter of*the*NEPS of bipartite*graphs*(Note) 226 (2001) 373}376 Bryant, D.E., see P.*Adams*223 (2000) 1} 12 Cai, L., D. Corneil and A. ...##
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Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters

2018
*
Physical Review Fluids
*

A small coherent subset of

doi:10.1103/physrevfluids.3.113501
fatcat:4afgrtppwjdxth4h7utvnhaf7a
*the*pseudo-trajectories is obtained in this way consisting of those Lagrangian particles that are trapped*for*long times in*the*core of*the*superstructure*circulation*rolls and ... Weights at*the*edges of*the**graph*are determined by a mean dynamical distance between different particle trajectories. ... Acknowledgments*The*work of CS and AP is supported by*the*Priority Programme*on*Turbulent Superstructures of*the*Deutsche Forschungsgemeinschaft within Grant No. SPP 1881. ...##
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Eigenvalues of Cayley graphs
[article]

2019
*
arXiv
*
pre-print

We survey some of

arXiv:1809.09829v2
fatcat:57hq3pcaurhybgfuzzh6qi74nu
*the*known results*on*eigenvalues of Cayley*graphs*and their applications, together with related results*on*eigenvalues of Cayley digraphs and generalizations of Cayley*graphs*. ... So a*circulant**graph*Cay(Z n , S) satisfies*the**spectral**Ádám**property*if and only if,*for*any*circulant**graph*Cay(Z n , T ), Spec(Cay(Z n , S)) = Spec(Cay(Z n , T )) implies Cay(Z n , S) ∼ = Cay(Z n , ... [231] proposed to study*the*following problem: "Which*circulant**graphs*Cay(Z n , S) satisfy*the**spectral**Ádám**property*, that is,*for*any T ⊆ Z n satisfying 0 ∈ T = −T , Spec(Cay(Z n , S)) = Spec(Cay ...##
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Learning Local Receptive Fields and their Weight Sharing Scheme on Graphs
[article]

2017
*
arXiv
*
pre-print

We propose a simple and generic layer formulation that extends

arXiv:1706.02684v3
fatcat:jmnggfa7hzfmngi65ji4zfslnm
*the**properties*of convolutional layers to any domain that can be described by a*graph*. ... Namely, we use*the*support of its adjacency matrix to design learnable weight sharing filters able to exploit*the*underlying structure of signals in*the*same fashion as*for*images. ...*For*non-*spectral*approaches, feature correspondences in*the*input domain allow to define how*the*weights are tied across*the*layer, such as*for*images or manifolds. ...
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