The Rotor-Router Group of Directed Covers of Graphs
نویسندگان
چکیده
A rotor-router walk is a deterministic version of a random walk, in which the walker is routed to each of the neighbouring vertices in some fixed cyclic order. We consider here directed covers of graphs (called also periodic trees) and we study several quantities related to rotor-router walks on directed covers. The quantities under consideration are: order of the rotor-router group, order of the root element in the rotor-router group and the connection with random walks.
منابع مشابه
Erratum: Transience and recurrence of rotor-router walks on directed covers of graphs
In the paper [4] Transience and recurrence of rotor-router walks on directed covers of graphs, published in ECP volume 17 (2012), no. 41 there is an error in the proof of Corollary 3.8. This corollary is essential for the transient part in the proof of Theorem 3.5(b). We fix this error by constructing a new rotor-router process, which fulfills our needs, and for which the statement of Corollary...
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The rotor-router model, also called the Propp machine, was introduced as a deterministic alternative to the random walk. In this model, a group of identical tokens are initially placed at nodes of the graph. Each node maintains a cyclic ordering of the outgoing arcs, and during consecutive turns the tokens are propagated along arcs chosen according to this ordering in round-robin fashion. The b...
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012