Fault-diameter of Cartesian graph bundles

Mixed fault diameter of Cartesian graph bundles II

“…We show by examples that the bounds of the new result are tight. In addition, in some cases Theorem 4.6 also improves previously known results on vertex and edge fault diameters on these classes of Cartesian graph bundles [2,5].…”

“…An upper bound for the mixed fault diameter of Cartesian graph bundles is given in [14] that in some case also improves previously known results on vertex and edge fault diameters on these classes of Cartesian graph bundles [2,5]. However these results address only the number of faults given by the connectivity of the fibre (plus one vertex), while the connectivity of the graph bundle can be much higher when the connectivity of B is substantial.…”

“…For example, [16,24] consider Hamiltonian properties assuming a combination of vertex and edge faults. In recent work on fault diameter of Cartesian graph products and bundles [2,3,4,5], analogous results were found for both fault diameter and edge fault diameter. However, the proofs for vertex and edge faults are independent, and our effort to see how results in one case may imply the others was not successful.…”

“…Clearly (k, ) is a connectivity pair of G exactly when: (1) G is (k − 1, )+connected, (2) G is (k, − 1)+connected, and (3) G is not (k, )+connected. In fact, as shown in [13], (2) implies (1), so (k, ) is a connectivity pair exactly when (2) and (3) hold.…”

“…A lot of work has been done on various aspects of network fault tolerance, see for example the survey [8] and the more recent papers [16,24,26]. In particular the fault diameter with faulty vertices, which was first studied in [18], and the edge fault diameter have been determined for many important networks recently [2,3,4,5,10,11,19,25]. Usually either only edge faults or only vertex faults are considered, while the case when both edges and vertices may be faulty is studied rarely.…”