Fault diameters of graph products and bundles

Fault tolerance and transmission delay of networks are important concepts in network design. The notions are strongly related to connectivity and diameter of a graph, and have been studied by many authors. Wide diameter of a graph combines studying connectivity with the diameter of a graph. Diameter with width k of a graph G is defined as the minimum integer d for which there exist at least k internally disjoint paths of length at most d between any two distinct vertices in G. Fault diameters are diameters of a graph after some of its elements (vertices, edges, or both) are deleted. Cartesian graph products and Cartesian graph bundles are among frequently studied interconnection network topologies. A brief survey of results on fault tolerance parameters of these graph families is given. Key–Words: interconnection network, fault tolerance, vertex connectivity, edge connectivity, mixed connectivity, vertex fault-diameter, edge fault-diameter, mixed fault-diameter, wide diameter, Cartesian graph bundle, Cartesian graph product, product graph.