Minimal Feedback Vertex Sets in Honeycomb Networks

Abstract

A vertex subset of a graph G is called a feedback vertex set if its removal results in an acyclic subgraph. The feedback vertex number ( ) G  is the cardinality of the minimum feedback vertex set of G , which is an important parameter of interconnection network topology. In this paper, we determine the feedback numbers of Honeycomb mesh n HM and Honeycomb torus n HT , i.e. 2 ( ) 9 / 2 15n/2 4 n HM n     and 2 / ( 2 ) 9 9 / 2 2 n HT n n     . Comparing these results with those of Zhou, we find that ( ) H  is related to the boundary of Honeycomb network H .