Abstract
The vertex boundary-width problem (for short VBWP) is to determine the value of vbw ( G ) = max 1 ⩽ ℓ ⩽ | V | min S ⊆ V , | S | = ℓ | N ( S ) | for a given graph G = ( V , E ) , where N ( S ) = { v ∉ S | v is a neighbor of u for some u ∈ S } . In this paper, we give a lower bound for vertex boundary-width of complete k-ary trees.
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