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On the spectral Ádám property for circulant graphs
2002
Discrete Mathematics
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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]
1998
Lecture Notes in Computer Science
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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
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) ;
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
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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
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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]
2007
arXiv
pre-print
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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]
2019
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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]
2020
arXiv
pre-print
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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
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, 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
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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
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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
2018
Physical Review Fluids
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2018 pre-print arXiv:1810.07396v1 fatcat:t3c224gmyjbnxiglclf6rks7cm
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]
2019
arXiv
pre-print
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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]
2017
arXiv
pre-print
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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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