A note on the order of iterated line digraphs

29 Jul 2016  ·  Dalfó C., Fiol M. A. ·

Given a digraph $G$, we propose a new method to find the recurrence equation for the number of vertices $n_k$ of the $k$-iterated line digraph $L^k(G)$, for $k\geq0$, where $L^0(G)=G$. We obtain this result by using the minimal polynomial of a quotient digraph $\pi(G)$ of $G$... We show some examples of this method applied to the so-called cyclic Kautz, the unicyclic, and the acyclic digraphs. In the first case, our method gives the enumeration of the ternary length-2 squarefree words of any length. read more

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Combinatorics