3 research outputs found
Wide diameter of Cartesian graph bundles
No full textFault 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 â–«â–« of a graph â–«â–«, â–«â–«-diameter, is defined as the minimum integer â–«â–« for which there exist at least â–«â–« internally disjoint paths of length at most â–«â–« between any two distinct vertices in â–«â–«. Denote by â–«â–« the â–«â–«-diameter of â–«â–« and â–«â–« the connectivity of â–«â–«. In the context of computer networks, wide diameters of Cartesian graph products have been recently studied by many authors. Cartesian graph bundles is a class of graphs that is a generalization of the Cartesian graph products. Let â–«â–« be a Cartesian graph bundle with fiber â–«â–« over base â–«â–«, â–«â–«, and â–«â–«. We prove that â–«â–«. Moreover, if â–«â–« is a graph bundle with fiber â–«â–« over base â–«â–«, then â–«â–«. The bounds are tight
