Results 251 to 260 of about 440,322 (281)

Eigenvectors of Distance-Regular Graphs

SIAM Journal on Matrix Analysis and Applications, 1988
The author studies the set of points the coordinates of which are rows of the matrix in which the columns are orthogonal eigenvectors associated to an eigenvalue of the adjacency matrix of a graph. In particular, the second largest eigenvalue \(\alpha\) and distance-regular graphs G are considered.
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Eigenpolytopes of Distance Regular Graphs

Canadian Journal of Mathematics, 1998
AbstractLet X be a graph with vertex set V and let A be its adjacency matrix. If E is the matrix representing orthogonal projection onto an eigenspace of A with dimension m, then E is positive semi-definite. Hence it is the Gram matrix of a set of |V| vectors in Rm. We call the convex hull of a such a set of vectors an eigenpolytope of X.
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Distance-regular Graphs of the Height h

Graphs and Combinatorics, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Bounding the diameter of distance-regular graphs

Combinatorica, 1988
Let G be a connected distance regular graph with valence \(k>2\) and diameter d. Suppose further that G is not a complete multipartite graph. let \(\theta\) be an eigenvalue of G with \(\theta \neq Ik,\) and \(m>1\). Then there are only finitely many connected, co-connected distance regular graphs with an eigenvalue of multiplicity m.
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Potential Theory on Distance-Regular Graphs

Combinatorics, Probability and Computing, 1993
A graph may be regarded as an electrical network in which each edge has unit resistance. We obtain explicit formulae for the effective resistance of the network when a current enters at one vertex and leaves at another in the distance-regular case.
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Distance-regular graphs

1978
Inequalities are obtained between the various parameters of a distance-regular graph. In particular, if k1 is the valency and k2 is the number of vertices at distance two from a given vertex, then in general k1 ⩽ k2. For distance-regular graphs of diameter at least four, k1=k2 if and only if the graph is simply a circuit.
D. E. Taylor, Richard Levingston
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A Bound for the Diameter of Distance-Regular Graphs

Combinatorica, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Distance-Regular Graphs

1989
Brouwer, A.E., Cohen, A.M., Neumaier, A.
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An inequality involving the second largest and smallest eigenvalue of a distance-regular graph

Linear Algebra and Its Applications, 2011
Jack Koolen, Jongyook Park
exaly  

The uniqueness of a distance-regular graph with intersection array $$\{32,27,8,1;1,4,27,32\}$$ { 32 , 27 , 8 , 1 ; 1 , 4 , 27 , 32 } and related results

Designs, Codes, and Cryptography, 2016
Leonard H Soicher
exaly