(k,+)-distance-hereditary graphs

https://doi.org/10.1016/S1570-8667(03)00030-3Get rights and content
Under an Elsevier user license
open archive

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.

Keywords

Interconnection networks
Dilation number
Distance-hereditary graphs
Characterization of graph classes
Forbidden subgraphs
Recognition algorithms

Cited by (0)

A preliminary version of this paper has been presented in [S. Cicerone, G. D'Ermiliis, G. Di Stefano, in: Proc. 27th International Workshop on Graph-Theoretic Concepts in Computer Science (WG '01), in: Lecture Notes in Comput. Sci., Vol. 2204, Springer, Berlin, 2001, pp. 66–77]. Partially supported by the Human Potential Programme of the European Union under contract no. HPRN-CT-1999-00104 (AMORE) and by the Italian MURST Project “Teoria dei Grafi ed Applicazioni”.