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| Main Author: | |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1910.12355 |
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Table of Contents:
- We deal in this work with a class of graphs, namely, the class of distance-regular graphs, in which on the basis of $k$-adjacency operators, the adjacency operator $A$ of a distance-regular graph is identified as a Jacobi matrix. To get so, the set of the $k$-adjacency operators is recognized as a canonical basis in a certain Hilbert space, where the spectrum of the Jacobi matrix coincides with the support of the measure of $A$. The obtained identification permits a deeper spectral analysis of the graph. The finite-dimensional case is addressed by means of the extension theory of nondensely defined, symmetric linear operators.