**On spectral constructions for Salem graphs.** / Gumbrell, Lee.

Research output: Thesis › Doctoral Thesis

Unpublished

**On spectral constructions for Salem graphs.** / Gumbrell, Lee.

Research output: Thesis › Doctoral Thesis

Gumbrell, L 2013, 'On spectral constructions for Salem graphs', Ph.D., Royal Holloway, University of London.

Gumbrell L. On spectral constructions for Salem graphs. 2013. 102 p.

@phdthesis{9b8b2cbcf46e4f6597b06f8c86078fdb,

title = "On spectral constructions for Salem graphs",

abstract = "In recent years, people have begun studying Salem numbers by looking at the spectrum of the adjacency matrix of a graph. In this thesis we classify infinitely many new infinite families of Salem graphs using results about graph spectra. Our first method is to define a notion of how close a Salem graph is to being cyclotomic, the m-Salem graphs, and classify the whole family of 1-Salem graphs. The second method uses the Courant-Weyl inequalities in a novel way, partitioning the edges of a graph into two sets and considering the graphs they form. We exhaustively work through all possibilities to find even more families of Salem graphs. We also study when some of these graphs produce trivial Salem numbers, using a new extension of Hoffman and Smith's subdivision theorem.",

author = "Lee Gumbrell",

year = "2013",

language = "English",

school = "Royal Holloway, University of London",

}

TY - THES

T1 - On spectral constructions for Salem graphs

AU - Gumbrell, Lee

PY - 2013

Y1 - 2013

N2 - In recent years, people have begun studying Salem numbers by looking at the spectrum of the adjacency matrix of a graph. In this thesis we classify infinitely many new infinite families of Salem graphs using results about graph spectra. Our first method is to define a notion of how close a Salem graph is to being cyclotomic, the m-Salem graphs, and classify the whole family of 1-Salem graphs. The second method uses the Courant-Weyl inequalities in a novel way, partitioning the edges of a graph into two sets and considering the graphs they form. We exhaustively work through all possibilities to find even more families of Salem graphs. We also study when some of these graphs produce trivial Salem numbers, using a new extension of Hoffman and Smith's subdivision theorem.

AB - In recent years, people have begun studying Salem numbers by looking at the spectrum of the adjacency matrix of a graph. In this thesis we classify infinitely many new infinite families of Salem graphs using results about graph spectra. Our first method is to define a notion of how close a Salem graph is to being cyclotomic, the m-Salem graphs, and classify the whole family of 1-Salem graphs. The second method uses the Courant-Weyl inequalities in a novel way, partitioning the edges of a graph into two sets and considering the graphs they form. We exhaustively work through all possibilities to find even more families of Salem graphs. We also study when some of these graphs produce trivial Salem numbers, using a new extension of Hoffman and Smith's subdivision theorem.

M3 - Doctoral Thesis

ER -