The β-Rauzy graph of order k for any infinite word is a directed graph
in which an arc (v1β,v2β) is formed if the concatenation of the word v1β
and the suffix of v2β of length kββ is a subword of the infinite word.
In this paper, we consider one of the important aperiodic recurrent words, the
infinite Fibonacci word for discussion. We prove a few basic properties of the
β-Rauzy graph of the infinite Fibonacci word. We also prove that the
β-Rauzy graphs for the infinite Fibonacci word are strongly connected.Comment: 10 pages, 4 figure