A generalization of Fiedler's lemma and some applications

Abstract

In a previous paper [M. Robbiano, E.A. Martins, and I. Gutman, Extending a theorem by Fiedler and applications to graph energy, MATCH Commun. Math. Comput. Chem. 64 (2010), pp. 145–156], a lemma by Fiedler was used to obtain eigenspaces of graphs, and applied to graph energy. In this article Fiedler's lemma is generalized and this generalization is applied to graph spectra and graph energy.

Keywords:

• graph spectrum
• graph energy

AMS Subject Classifications:

• 05C50
• 15A18

Acknowledgements

The research of Domingos M. Cardoso and Enide Andrade Martins was supported by Centre for Research and Development in Mathematics and Applications (CIDMA) from the ‘Fundação para a Ciência e a Tecnologia – FCT’, cofinanced by the European Community Fund FEDER/POCI 2010 and Project Graph Spectra and Applications with reference PTDC/MAT/112276/2009. María Robbiano thanks Comisión Nacional de Investigación Científica y Tecnológica CONICYT for support of this work, through the Proyecto FONDECYT IC No. 11090211.