Small regular graphs with four eigenvalues

Abstract

General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research-You may not further distribute the material or use it for any profit-making activity or commercial gain-You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim.

Graphs with four distinct Laplacian eigenvalues

“…For results on nonregular graphs with three adjacency eigenvalues, we refer the reader to [1,3,5,16]. Regular graphs with four adjacency (Laplacian) eigenvalues were studied in [6,10], and nonregular bipartite graphs with four adjacency eigenvalues were investigated in [8,9], through the study of the incidence graphs of some combinatorial designs.…”

A Nonregular Analogue of Conference Graphs

“…This forces some structural restrictions on G[X ] (cf. [5,7]); for example, it must be walk-regular.…”

Graphs with two main and two plain eigenvalues

“…The connected non-regular graphs with three distinct eigenvalues have been studied by, for example, De Caen, Van Dam & Spence [7], Bridges & Mena [1], Muzychuk & Klin [13], Van Dam [17] and Cheng, Gavrilyuk, Greaves & Koolen [6]. The connected regular graphs with four distinct eigenvalues were studied by Van Dam [18], Van Dam & Spence [19] and Huang & Huang [12], among others. Cioabă, Haemers, Vermette & Wong [4] (resp.…”