Author: Steve Kirkland
Publisher: Taylor & Francis Ltd
ISSN: 0308-1087
Source: Linear and Multilinear Algebra, Vol.52, Iss.2, 2004-03, pp. : 79-98
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Abstract
We describe the graphs having the property that adding a particular edge will result in exactly two Laplacian eigenvalues increasing by 1 and the other Laplacian eigenvalues remaining fixed. For a certain subclass of graphs, we also characterize the Laplacian integral graphs with that property. Finally, we investigate a situation in which the algebraic connectivity is one of the eigenvalues that increases by 1.
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