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    <title>Graph powers</title>
    <subTitle>hardness results, good characterizations and efficient algorithms</subTitle>
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    <namePart>Nguyen, Ngoc Tuy</namePart>
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  <abstract type="Summary">Given a graph H = (V_H,E_H) and a positive integer k, the k-th power of H, written H^k, is the graph obtained from H by adding edges between any pair of vertices at distance at most k in H; formally, H^k = (V_H, {xy | 1 &lt;= d_H (x, y) &lt;= k}). A graph G is the k-th power of a graph H if G = H^k, and in this case, H is a k-th root of G. Our investigations deal with the computational complexity of recognizing k-th powers of general graphs as well as restricted graphs. This work provides new NP-completeness results, good characterizations and efficient algorithms for graph powers.</abstract>
  <note type="statement of responsibility">vorgelegt von Ngoc Tuy Nguyen</note>
  <note type="thesis">Rostock, Univ., Fak. f. Informatik u. Elektrotechnik, Diss., 2009</note>
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