PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Wide diameter of Cartesian graph bundles.
Iztok Banič and Janez Žerovnik
Discrete math. Volume 310, Number 12, pp. 1697-1701, 2010.

Abstract

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, k-diameter, 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. Denote by the c-diameter of G and κ(G) the connectivity of G. 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 G be a Cartesian graph bundle with fiber F over base B, 0<a≤κ(F), and 0<b≤κ(B). We prove that . Moreover, if G is a graph bundle with fiber F≠K2 over base B≠K2, then . The bounds are tight.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:7084
Deposited By:Igor Pesek
Deposited On:01 March 2011