(k, +)-Distance-Hereditary Graphs

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.