Feedback Numbers of Balanced Hypercubes BH_n

Abstract

A subset of vertices of a graph G is called a feedback vertex set of G if its removal results in an acyclic subgraph. We use f(BHn) to denote the feedback number of balanced hypercubes BHn. In this paper, we construct a feedback vertex set of BHn and obtain ⌜2^2^n-1) (1-1/(2n-1)+1/2n-1 ⌝ ≤ f(BH_n ) ≤ 2^2^n-1- 2^n-1 for n ≤ 3 and ⌜2^2^n-1) (1-1/(2n-1)+1/(2n-1) ⌝ ≤ f(BH n ) ≤ 2^2^n-1) -2^n for n ≥ 4.