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On the spectral Ádám property for circulant graphs

Bernard Mans, Francesco Pappalardi, Igor Shparlinski
2002 Discrete Mathematics  
We investigate a certain condition 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] .  ... 
doi:10.1016/s0012-365x(01)00374-0 fatcat:miyhjgzhtzbvjirfxtyaeb2qzu

On the Ádám Conjecture on Circulant Graphs [chapter]

Bernard Mans, Francesco Pappalardi, Igor Shparlinski
1998 Lecture Notes in Computer Science  
We investigate 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.  ... 
doi:10.1007/3-540-68535-9_29 fatcat:7dmt5mjqv5f4dhsz2g6l5rceou

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).  ... 

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.  ... 

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

Doug Wiedemann, Michael Zieve
2007 arXiv   pre-print
We also explain how our problem relates to 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.  ... 
arXiv:0706.1567v1 fatcat:2dtoegn4p5e6padmoct7zxqvbu

Spectrum of some arrow-bordered circulant matrix [article]

Wojciech Florek, Adam Marlewski
2019 arXiv   pre-print
We find its eigenpairs and we discuss its spectrum with stress 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.  ... 
arXiv:1905.04807v1 fatcat:oomn7ukubrcnlnhvsoiyjxakqe

Learning Algebraic Multigrid Using Graph Neural Networks [article]

Ilay Luz, Meirav Galun, Haggai Maron, Ronen Basri, Irad Yavneh
2020 arXiv   pre-print
Efficient numerical solvers 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.  ... 
arXiv:2003.05744v2 fatcat:2pdfjvtggvga3dwoa3dgo226ye

Improving Expressivity of Graph Neural Networks [article]

Stanisław Purgał
2020 arXiv   pre-print
We propose a 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.  ... 
arXiv:2004.05994v1 fatcat:3mqnv7zlgbdqbe3ttqgl4mpsru

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]

Jason Kaye, Hugo U. R. Strand
2021 arXiv   pre-print
We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, 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).  ... 
arXiv:2110.06120v1 fatcat:utb7i4lo2jf2tapwnhibxkky64

Master index of volumes 221-230

2001 Discrete Mathematics  
Yebra, Boundary 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.  ... 
doi:10.1016/s0012-365x(01)00058-9 fatcat:xoeto3fhfra5dhyjrww2tymguu

Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters

Christiane Schneide, Ambrish Pandey, Kathrin Padberg-Gehle, Jörg Schumacher
2018 Physical Review Fluids  
A small coherent subset of 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.  ... 
doi:10.1103/physrevfluids.3.113501 fatcat:4afgrtppwjdxth4h7utvnhaf7a

Eigenvalues of Cayley graphs [article]

Xiaogang Liu, Sanming Zhou
2019 arXiv   pre-print
We survey some of 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  ... 
arXiv:1809.09829v2 fatcat:57hq3pcaurhybgfuzzh6qi74nu

Learning Local Receptive Fields and their Weight Sharing Scheme on Graphs [article]

Jean-Charles Vialatte, Vincent Gripon, Gilles Coppin
2017 arXiv   pre-print
We propose a simple and generic layer formulation that extends 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.  ... 
arXiv:1706.02684v3 fatcat:jmnggfa7hzfmngi65ji4zfslnm
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