Results 271 to 280 of about 179,652 (285)
The Spectrum of an Infinite Graph
Canadian Journal of Mathematics, 2000 AbstractIn 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)
Hajime Urakawa
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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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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,
Risi Kondor, Karsten M. Borgwardt
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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,
Risi Kondor, Karsten M. Borgwardt
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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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The Laplacian Spectrum of a Graph II
SIAM Journal on Discrete Mathematics, 1994Summary: [For Part I see \textit{R. Grone}, \textit{R. Merris} and \textit{V. S. Sunder}, SIAM J. Matrix Anal. Appl. 11, No. 2, 218-238 (1990; Zbl 0733.05060).] Let \(G\) be a graph. Denote by \(D(G)\) the diagonal matrix of its vertex degrees and by \(A(G)\) its adjacency matrix. Then \(L(G) = D(G) -A(G)\) is the Laplacian matrix of \(G\).
Robert Grone, Russell Merris
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The Spectrum of the Corona of Two Graphs
SIAM Journal on Discrete Mathematics, 2007We consider only simple graphs. Given two graphs $G$ with vertices $1,\ldots,n$ and $H$, the corona $G\circ H$ is defined as the graph obtained by taking $n$ copies of $H$ and for each $i$ inserting edges between the $i$th vertex of $G$ and each vertex of the $i$th copy of $H$. For a connected graph $G$ and any $r$-regular graph $H$ we provide complete
Sasmita Barik +2 more
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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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The spectrum problem for the Petersen graph
Journal of Graph Theory, 1996Summary: It is shown that there exists a decompositon of \(K_v\) into edge-disjoint copies of the Petersen graph if and only if \(v\equiv 1\) or \(10\pmod{15}\), \(v\neq 10\).
Peter Adams 0001, Darryn E. Bryant
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On the spectrum of projective norm-graphs
Information Processing Letters, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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