Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  4 Oct 1996 
Place of Publication  Tilburg 
Publisher  
Publication status  Published  1996 
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Graphs with few eigenvalues. An interplay between combinatorics and algebra. / van Dam, E.R.
Tilburg : CentER, Center for Economic Research, 1996. 146 p.Research output: Thesis › Doctoral Thesis › Scientific
TY  THES
T1  Graphs with few eigenvalues. An interplay between combinatorics and algebra
AU  van Dam, E.R.
PY  1996
Y1  1996
N2  Two standard matrix representations of a graph are the adjacency matrix and the Laplace matrix. The eigenvalues of these matrices are interesting parameters of the graph. Graphs with few eigenvalues in general have nice combinatorial properties and a rich structure. A well investigated family of such graphs comprises the strongly regular graphs (the regular graphs with three eigenvalues), and we may see other graphs with few eigenvalues as algebraic generalizations of such graphs. We study the (nonregular) graphs with three adjacency eigenvalues, graphs with three Laplace eigenvalues, and regular graphs with four eigenvalues. The last ones are also studied in relation with threeclass association schemes. We also derive bounds on the diameter and on the size of special subsets in terms of the eigenvalues of the graph. Included are lists of feasible parameter sets of graphs with three Laplace eigenvalues, regular graphs with four eigenvalues, and threeclass association schemes.
AB  Two standard matrix representations of a graph are the adjacency matrix and the Laplace matrix. The eigenvalues of these matrices are interesting parameters of the graph. Graphs with few eigenvalues in general have nice combinatorial properties and a rich structure. A well investigated family of such graphs comprises the strongly regular graphs (the regular graphs with three eigenvalues), and we may see other graphs with few eigenvalues as algebraic generalizations of such graphs. We study the (nonregular) graphs with three adjacency eigenvalues, graphs with three Laplace eigenvalues, and regular graphs with four eigenvalues. The last ones are also studied in relation with threeclass association schemes. We also derive bounds on the diameter and on the size of special subsets in terms of the eigenvalues of the graph. Included are lists of feasible parameter sets of graphs with three Laplace eigenvalues, regular graphs with four eigenvalues, and threeclass association schemes.
M3  Doctoral Thesis
T3  CentER Dissertation Series
PB  CentER, Center for Economic Research
CY  Tilburg
ER 