The $k$-adjacency operators and adjacency Jacobi matrix on distance-regular graphs
Mathematical Physics
2024-05-17 v2 math.MP
Abstract
We deal in this work with a class of graphs, namely, the class of distance-regular graphs, in which on the basis of -adjacency operators, the adjacency operator of a distance-regular graph is identified as a Jacobi matrix. To get so, the set of the -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 . 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.
Cite
@article{arxiv.1910.12355,
title = {The $k$-adjacency operators and adjacency Jacobi matrix on distance-regular graphs},
author = {Josué I. Rios-Cangas},
journal= {arXiv preprint arXiv:1910.12355},
year = {2024}
}