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On the Multiplicities of Graph Eigenvalues
Author(s) -
Bell F. K.,
Rowlinson P.
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002030
Subject(s) - mathematics , combinatorics , codimension , eigenvalues and eigenvectors , upper and lower bounds , graph , distance regular graph , regular graph , quadratic equation , strongly regular graph , discrete mathematics , voltage graph , line graph , pure mathematics , graph power , mathematical analysis , geometry , physics , quantum mechanics
Star complements and associated quadratic functions are used to obtain a sharp upper bound for the order of a graph with an eigenspace of prescribed codimension. It is shown that for regular graphs the bound can be reduced by 1, and that this reduced bound is attained by a regular graph G if and only if G is an extremal strongly regular graph. 2000 Mathematics Subject Classification 05C50.