Geodesic
A necessary and sufficient eigenvector condition for a connected graph to be bipartite
The electronic journal of linear algebra, Tome 20 (2010), pp. 351-353.

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

Summary: We give a necessary and sufficient condition for a graph to be bipartite in terms of an eigenvector corresponding to the largest eigenvalue of the adjacency matrix of the graph.
Classification : 05C50, 15A18
Keywords: graph, bipartite, principal eigenvector, independent set 
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     title = {A necessary and sufficient eigenvector condition for a connected graph to be bipartite},
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Cioaba, Sebastian M. A necessary and sufficient eigenvector condition for a connected graph to be bipartite. The electronic journal of linear algebra, Tome 20 (2010), pp. 351-353. http://geodesic.mathdoc.fr/item/ELA_2010__20__a28/