# Discrete Mathematics & Theoretical Computer Science

## Volume 6 n° 1 (2003), pp. 123-132

author: | Selma Djelloul and Mekkia Kouider |
---|---|

title: | Minimum survivable graphs with bounded distance increase |

keywords: | distance, fault-tolerance, spanning subgraph |

abstract: | We study in graphs properties related to fault-tolerance in case a node fails. A graph G is k-self-repairing, where k is
a non-negative integer, if after the
removal of any vertex no distance in the surviving
graph increases by more than k.
In the design of interconnection networks such
graphs guarantee good fault-tolerance properties.
We give upper and lower bounds on the minimum
number of edges of a k-self-repairing graph for
prescribed k and n, where n is the order of
the graph. We prove that the problem of finding,
in a k-self-repairing graph, a spanning
k-self-repairing subgraph of minimum size
is NP-Hard.
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reference: | Selma Djelloul and Mekkia Kouider (2003),
Minimum survivable graphs with bounded distance increase,
Discrete Mathematics and Theoretical Computer Science 6, pp. 123-132 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Tue Nov 4 10:51:55 CET 2003 by falk