The $k$-adjacency operators and adjacency Jacobi matrix on distance-regular graphs
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866917667140534272 |
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| author | Rios-Cangas, Josué I. |
| author_facet | Rios-Cangas, Josué I. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_12355 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The $k$-adjacency operators and adjacency Jacobi matrix on distance-regular graphs Rios-Cangas, Josué I. Mathematical Physics 05C63, 34L05, 47B36 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. |
| title | The $k$-adjacency operators and adjacency Jacobi matrix on distance-regular graphs |
| topic | Mathematical Physics 05C63, 34L05, 47B36 |
| url | https://arxiv.org/abs/1910.12355 |