A lower bound for the vertex boundary-width of complete k-ary trees

The vertex boundary-width problem (for short VBWP) is to determine the value of vbw(G) = max(1 <= l <= vertical bar V vertical bar) min (S subset of V,vertical bar S vertical bar=l)vertical bar N(S)vertical bar for a given graph G = (V, E), where N(S) = {upsilon is not an element of S vertical bar upsilon is a neighbor of u for some u is an element of S}. In this paper, we give a lower bound for vertex boundary-width of complete k-ary trees. (C) 2007 Elsevier B.V. All rights reserved.