In mathematics, in graph theory, the Seidel adjacency matrix of a simple undirected graph G is a symmetric matrix with a row and column for each vertex, having 0 on the diagonal, −1 for positions whose rows and columns correspond to adjacent vertices, and +1 for positions corresponding to non-adjacent vertices.
It is also called the Seidel matrix or—its original name—the (−1,1,0)-adjacency matrix.
It can be interpreted as the result of subtracting the adjacency matrix of G from the adjacency matrix of the complement of G.
The multiset of eigenvalues of this matrix is called the Seidel spectrum.
The Seidel matrix was introduced by J. H. van Lint and Johan Jacob Seidel [de; nl] in 1966 and extensively exploited by Seidel and coauthors.
The Seidel matrix of G is also the adjacency matrix of a signed complete graph KG in which the edges of G are negative and the edges not in G are positive. It is also the adjacency matrix of the two-graph associated with G and KG.
The eigenvalue properties of the Seidel matrix are valuable in the study of strongly regular graphs.
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In mathematics, in graph theory, the Seideladjacencymatrix of a simple undirected graph G is a symmetric matrix with a row and column for each vertex...
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girth-5 Moore graphs except the ones listed above. Partial geometry Seideladjacencymatrix Two-graph Brouwer, Andries E; Haemers, Willem H. Spectra of Graphs...
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{\displaystyle n} vertices such that all of the eigenvalues of its adjacencymatrix A G {\displaystyle A_{G}} except one have absolute value at most λ...
integers'. V. I. Arnold rediscovered Seidel's algorithm and later Millar, Sloane and Young popularized Seidel's algorithm under the name boustrophedon...
Wolfram Web Resource. Retrieved 2009-08-13. J. J. Seidel, Strongly regular graphs with (−1,1,0) adjacencymatrix having eigenvalue 3, Lin. Alg. Appl. 1 (1968)...
1088/1464-4258/9/3/001. Conforti, G. (1983). "Zernike aberration coefficients from Seidel and higher-order power-series coefficients". Opt. Lett. 8 (7): 407–408....
{\displaystyle O(n\log h)} . These include Chan's algorithm and the Kirkpatrick–Seidel algorithm. For dimensions d > 3 {\displaystyle d>3} , the time for computing...
Archived from the original on December 22, 2018. Retrieved December 22, 2018. Seidel, Jeff (April 6, 2017). "Joe Louis Arena: Saying good-bye to the heart of...
culturing models. This work focused on the importance of the extracellular matrix and the ability of cultures in artificial 3D matrices to produce physiologically...
Shimbel (1953), who observed that it could be solved by a linear number of matrix multiplications that takes a total time of O(V4). Shortest path algorithms...
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Psychological Review, 63 (5): 277–293, doi:10.1037/h0046049, PMID 13359597. Seidel, J. J. (1976), "A survey of two-graphs", Colloquio Internazionale sulle...
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