The spectral excess theorem for graphs with few eigenvalues whose distance-2 or distance-1-or-2 graph is strongly regular

Autor: J. Koolen, Cristina Dalfó, Miguel Angel Fiol

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Linear and Multilinear Algebra
Recercat. Dipósit de la Recerca de Catalunya
instname
Repositorio Abierto de la UdL
Universitad de Lleida

We study regular graphs whose distance-2 graph or distance-1-or-2 graph is strongly regular. We provide a characterization of such graphs Γ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the mean number of vertices

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1732ed0c078ccefd6148c475ad1adfb3

The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues

Autor: Miguel Angel Fiol

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname

The final publication is available at Springer via http://dx.doi.org/10.1007/s10801-015-0654-6 Let Gamma be a distance-regular graph with diameter d and Kneser graph K = Gamma(d), the distance-d graph of Gamma. We say that Gamma is partially antipoda

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29db660bc72a752a1aa01c7eed82f93f
http://hdl.handle.net/2117/100474

Pseudo-distance-regularized graphs are distance-regular or distance-biregular

Autor: Miguel Angel Fiol

Publikováno v: Linear Algebra and its Applications. 437:2973-2977

The concept of pseudo-distance-regularity around a vertex of a graph is a natural generalization, for non-regular graphs, of the standard distance-regularity around a vertex. In this note, we prove that a pseudo-distance-regular graph around each of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9473bf73c6bde91d6809052ad8e14809
https://doi.org/10.1016/j.laa.2012.07.019

A simple proof of the spectral excess theorem for distance-regular graphs

Autor: E. Garriga, Silvia Gago, Miquel Àngel Fiol

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)

The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each of its vertices. The origina

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::adb9d1386c5896c144c17193f36a2bb1

Algebraic characterizations of regularity properties in bipartite graphs

Autor: Miguel Angel Fiol, Cristina Dalfó, Aida Abiad

Publikováno v: UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
European Journal of Combinatorics, 34(8), 1223-1231. Academic Press Inc.
Recercat. Dipósit de la Recerca de Catalunya
instname

Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph GG is distance-regular if and only if its spectral excess (a number that can be computed from th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b4e0f41482a96bdca1623c13357f2c4