(k, +)-distance-hereditary graphs

Authors:
Serafino Cicerone;Gabriele Di Stefano
Affiliations:
Dipartimento di Ingegneria Elettrica, Università degli Studi dell'Aquila, I-67040 Monteluco di Roio, L'Aquila, Italy;Dipartimento di Ingegneria Elettrica, Università degli Studi dell'Aquila, I-67040 Monteluco di Roio, L'Aquila, Italy
Venue:
Journal of Discrete Algorithms
Year:
2003

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Abstract

In this work we introduce, characterize, and provide algorithmic results for (k, +)-distance-hereditary graphs, k ≥ 0. These graphs can be used to model interconnection networks with desirable connectivity properties; a network modeled as a (k, +)-distance-hereditary graph can be characterized as follows: if some nodes have failed, as long as two nodes remain connected, the distance between these nodes in the faulty graph is bounded by the distance in the non-faulty graph plus an integer constant k. The class of all these graphs is denoted by DH(k, +). By varying the parameter k, classes DH(k, +) include all graphs and form a hierarchy that represents a parametric extension of the well-known class of distance-hereditary graphs.