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Discrete Mathematics, 2023
The author of this paper obtains new bounds on the second eigenvalue of Johnson graphs and applies these bounds to obtain new results on the modularity of Johnson graphs and their random subgraphs, the Hamiltonicity of Johnson graphs, and thresholds of the appearance of the Hamilton cycles and giant components.
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The author of this paper obtains new bounds on the second eigenvalue of Johnson graphs and applies these bounds to obtain new results on the modularity of Johnson graphs and their random subgraphs, the Hamiltonicity of Johnson graphs, and thresholds of the appearance of the Hamilton cycles and giant components.
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2011
This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.
Brouwer, A.E., Haemers, W.H.
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This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.
Brouwer, A.E., Haemers, W.H.
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SPECTRUM BASED TECHNIQUES FOR GRAPH ISOMORPHISM
International Journal of Foundations of Computer Science, 2009The graph isomorphism problem is to check if two given graphs are isomorphic. Graph isomorphism is a well studied problem and numerous algorithms are available for its solution. In this paper we present algorithms for graph isomorphism that employ the spectra of graphs.
Rajasekaran, Sanguthevar, Kundeti, Vamsi
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Proceedings of the 25th international conference on Machine learning - ICML '08, 2008
The central issue in representing graph-structured data instances in learning algorithms is designing features which are invariant to permuting the numbering of the vertices. We present a new system of invariant graph features which we call the skew spectrum of graphs. The skew spectrum is based on mapping the adjacency matrix of any (weigted, directed,
Kondor, R. +1 more
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The central issue in representing graph-structured data instances in learning algorithms is designing features which are invariant to permuting the numbering of the vertices. We present a new system of invariant graph features which we call the skew spectrum of graphs. The skew spectrum is based on mapping the adjacency matrix of any (weigted, directed,
Kondor, R. +1 more
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The Spectrum of an Infinite Graph
Canadian Journal of Mathematics, 2000AbstractIn this paper, we consider the (essential) spectrum of the discrete Laplacian of an infinite graph. We introduce a new quantity for an infinite graph, in terms of which we give new lower bound estimates of the (essential) spectrum and give also upper bound estimates when the infinite graph is bipartite. We give sharp estimates of the (essential)
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1977
We survey the results obtained by a large number of authors concerning the spectrum of a graph. The questions of characterisation by spectrum, cospectral graphs and information derived from the spectrum are discussed.
C. Godsil, D. A. Holton, B. McKay
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We survey the results obtained by a large number of authors concerning the spectrum of a graph. The questions of characterisation by spectrum, cospectral graphs and information derived from the spectrum are discussed.
C. Godsil, D. A. Holton, B. McKay
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1973
PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/189737/2/7324678 ...
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PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/189737/2/7324678 ...
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Graphs with small fall-spectrum
Discrete Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Seidel spectrum of threshold graphs
Computational and Applied Mathematics, 2022Renata R. Del-Vecchio, Miriam Abdón
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