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# Which Digraphs with Ring Structure are Essentially Cyclic?

@article{Agaev2009WhichDW, title={Which Digraphs with Ring Structure are Essentially Cyclic?}, author={Rafig P. Agaev and Pavel Yu. Chebotarev}, journal={CoRR}, year={2009}, volume={abs/0910.3113} }

- Published 2009 in ArXiv
DOI:10.1016/j.aam.2010.01.005

We say that a digraph is essentially cyclic if its Laplacian spectrum is not completely real. The essential cyclicity implies the presence of directed cycles, but not vice versa. The problem of characterizing essential cyclicity in terms of graph topology is difficult and yet unsolved. Its solution is important for some applications of graph theory, including that in decentralized control. In the present paper, this problem is solved with respect to the class of digraphs with ring structure… CONTINUE READING