The set of sequence entropies for graph maps

Let X be a compact metric space and f : X → X be continuous. Let h ⁎ ( f ) be the supremum of sequence entropies over all subsequences of N . It is known that if X is a finite tree then h ⁎ ( f ) ∈ { ∞ , 0 , log 2 } . In this paper we focus on finite graph and obtain the same result. Namely, if X is a finite graph then h ⁎ ( f ) ∈ { 0 , log 2 , ∞ } .