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Abstract
This paper deals with several operations on graphs and combinatorial structures linking them with their associated Lie algebras. More concretely, our main goal is to obtain some criteria to determine when there exists a Lie algebra associated with a combinatorial structure arising from those operations. Additionally, we show an algorithmic method for one of those operations.
Acknowledgements
This work has been partially supported by MTM2010-19336 and FEDER. The authors thank the editor and the referees for their useful comments and suggestions, which have allowed us to improve the quality of the paper.