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On the Fastest Moving Off from a Vertex in Directed Regular Graphs

V. I. Trofimov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Let $\Gamma$ be a directed regular locally finite graph, and let $\overline\Gamma$ be the undirected graph obtained by forgetting the orientation of $\Gamma$. Let $x$ be a vertex of $\Gamma$ and let $n$ be a nonnegative integer. We study the length of the shortest directed path in $\Gamma$ starting at $x$ and ending outside of the ball of radius $n$ centered at $x$ in $\overline\Gamma$.

Keywords: directed graph, undirected graph, locally finite graph, automorphism group.

UDC: 519.17

Received: 06.05.2006
Revised: 10.04.2007

DOI: 10.4213/mzm4088

 English version: Mathematical Notes, 2007, 82:5, 691–702

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