Geodesic
Spectra of expansion graphs
The electronic journal of linear algebra, Tome 6 (1999-2000), pp. 2-10.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Replace certain edges of a directed graph by chains and consider the effect on the spectrum of the graph. It is shown that the spectral radius decreases monotonically with the expansion and that, for a strongly connected graph that is not a single cycle, the spectral radius decreases strictly monotonically with the expansion. A limiting formula is given for the spectral radius of the expanded graph when the lengths of some chains replacing the original edges tend to infinity. The proofs depend on the construction of auxiliary nonnegative matrices of the same size and with the same support as the original adjacency matrix.
Classification : 05C50, 15A18, 15A45, 05C20, 05C38
Keywords: graph expansion, graph spectrum 
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     title = {Spectra of expansion graphs},
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Friedland, Shmuel; Schneider, Hans. Spectra of expansion graphs. The electronic journal of linear algebra, Tome 6 (1999-2000), pp. 2-10. http://geodesic.mathdoc.fr/item/ELA_1999-2000__6__a0/