Selma Djelloul ; Mekkia Kouider - Minimum survivable graphs with bounded distance increase

dmtcs:338 - Discrete Mathematics & Theoretical Computer Science, January 1, 2003, Vol. 6 no. 1 - https://doi.org/10.46298/dmtcs.338
Minimum survivable graphs with bounded distance increase

Authors: Selma Djelloul ; Mekkia Kouider

    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.


    Volume: Vol. 6 no. 1
    Published on: January 1, 2003
    Imported on: March 26, 2015
    Keywords: distance,fault-tolerance,spanning subgraph,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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