Trees with a large Laplacian eigenvalue multiplicity

Autor: M.H. Fakharan, E.R. van Dam, Saieed Akbari

Publikováno v: Linear Algebra and its Applications, 586, 262-273. Elsevier Inc.

In this paper, we study the multiplicity of the Laplacian eigenvalues of trees. It is known that for trees, integer Laplacian eigenvalues larger than $1$ are simple and also the multiplicity of Laplacian eigenvalue $1$ has been well studied before. H

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8d108c4db1a2b484577206235c4dac60

Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.

Directed strongly walk-regular graphs

Autor: E.R. van Dam, Gholamreza Omidi

Publikováno v: Journal of Algebraic Combinatorics, 47(4). Springer Netherlands

We generalize the concept of strong walk-regularity to directed graphs. We call a digraph strongly $$\ell $$ -walk-regular with $$\ell > 1$$ if the number of walks of length $$\ell $$ from a vertex to another vertex depends only on whether the first

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f15ce111fddb927c9836e32ea485f430
https://doi.org/10.1007/s10801-017-0789-8

Some spectral and quasi-spectral characterizations of distance-regular graphs

Autor: E.R. van Dam, Miguel Angel Fiol, Aida Abiad

Publikováno v: Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics, 143, 1-18. Academic Press Inc.
Recercat. Dipósit de la Recerca de Catalunya
instname
Journal of Combinatorial Theory Series A, 143, 1-18. Academic Press Inc.
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6cbb0670a34ac8a37ca1333da213b8dc
https://research.tilburguniversity.edu/en/publications/4b8f3821-6159-4e1e-a9c2-e87f1ff0d688

On perturbations of almost distance-regular graphs

Autor: E.R. van Dam, Miguel Angel Fiol, Cristina Dalfó

Publikováno v: Linear Algebra and its Applications, 435(10), 2626-2638. Elsevier Inc.

In this paper we show that certain almost distance-regular graphs, the so-called $h$-punctually walk-regular graphs, can be characterized through the cospectrality of their perturbed graphs. A graph $G$ with diameter $D$ is called $h$-punctually walk

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::60af60fe1647ed9b80b53943656b082b
https://doi.org/10.1016/j.laa.2011.05.004