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An Inequality Involving the Local Eigenvalues of a Distance-Regular Graph

โœ Scribed by Paul Terwilliger

Book ID
111587716
Publisher
Springer
Year
2004
Tongue
English
Weight
224 KB
Volume
19
Category
Article
ISSN
0925-9899

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๐Ÿ“œ SIMILAR VOLUMES

Distance-Regular Graphs with an Eigenval
Distance-Regular Graphs with an Eigenvalue of Multiplicity Four
โœ R.R. Zhu ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 939 KB

Let \(G\) be a distance-regular graph. If \(G\) has an eigenvalue \(\theta\) of multiplicity \(m\) \((\geqslant 2)\), then \(G\) has a natural representation in \(R^{m}\). By studying the geometric properties of the image configuration in \(R^{m}\), we can obtain considerable information about the g

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The Local Structure of a Bipartite Distance-regular Graph
โœ Brian Curtin ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 285 KB

In this paper, we consider a bipartite distance-regular graph = (X, E) with diameter d โ‰ฅ 3. We investigate the local structure of , focusing on those vertices with distance at most 2 from a given vertex x. To do this, we consider a subalgebra R = R(x) of Mat X (C), where X denotes the set of vertice