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2008, Volume 2, Issue 4: 403-420. Doi: 10.3934/amc.2008.2.403
This issue Previous Article Lee weight enumerators of self-dual codes and theta functions Next Article On the construction of bent functions of $n+2$ variables from bent functions of $n$ variables

Discriminating codes in bipartite graphs: bounds, extremal cardinalities, complexity

  • 1.

    Institut TELECOM, TELECOM ParisTech, 46, rue Barrault, 75634 Paris Cedex 13

  • 2.

    Institut TELECOM - TELECOM ParisTech, & Centre National de la Recherche Scientifique - LTCI UMR 5141, 46, rue Barrault, 75634 Paris Cedex 13

Received:  May 2008
Revised:  October 2008
Published:  November 2008
Abstract / Introduction Related Papers Cited by
    Abstract
  • Consider an undirected bipartite graph $G=(V=I\cup A,E)$, with no edge inside $I$ nor $A$. For any vertex $v\in V$, let $N(v)$ be the set of neighbours of $v$. A code $C \subseteq A$ is said to be discriminating if all the sets $N(i) \cap C$, $i \in I$, are nonempty and distinct. We study some properties of discriminating codes. In particular, we give bounds on the minimum size of these codes, investigate graphs where minimal discriminating codes have size close to the upper bound, or give the exact minimum size in particular graphs; we also give an NP-completeness result.
    Mathematics Subject Classification: Primary: 05C99; Secondary: 94B65, 05C35, 68Q17.

    Citation:
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