## The Path-distance-width of Hypercubes

 Yota Otachi School of Information Science Japan Advanced Institute of Science and Technology Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan

## Abstract

The path-distance-width of a connected graph G is the minimum integer w satisfying that there is a nonempty subset of S ⊆ V(G) such that the number of the vertices with distance i from S is at most w for any nonnegative integer i.

In this note, we determine the path-distance-width of hypercubes.

Keywords: path-distance-width, hypercube

2010 Mathematics Subject Classification: 05C12, 05C76.

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Received 26 September 2011
Revised 25 April 2012
Accepted 5 July 2012