The Contradiction Argument for the Brouwer Conjecture

André Luis Andrejew Ferreira, Débora Marília Hauenstein, Guilherme Porto


In this work we develop results to contribute to the study of the Brouwer conjecturethrough an argument of contradiction. Specifically, if the Brouwer conjecture is not valid for agraph and this graph respects some conditions, we show that the conjecture is also not valid for thegraphs obtained by deleting an edge or vertex. In this way, we can recursively delete certain verticesand edges of the original graph until the resulting graph is in a family for which the conjecture isproven, a contradiction.


Brouwer Conjecture; Laplacian Eigenvalues; Spectral Graph Theory

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