Fault diameter of product graphs

The (k − 1)-fault diameter Dk(G) of a k-connected graph G is the maximum diameter of an induced subgraph by deleting at most k − 1 vertices from G. This paper considers the fault diameter of the product graph G1 ∗ G2 of two graphs G1 and G2 and proves that Dk1+k2 (G1 ∗ G2) Dk1 (G1) + Dk2 (G2) + 1 if G1 is k1-connected and G2 is k2-connected. This generalizes some known results such as Baniˇc and Žerovnik [I. Baniˇc, J. Žerovnik, Fault-diameter of Cartesian graph bundles, Inform. Process. Lett. 100 (2) (2006) 47–51]. © 2007 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Jun-Ming Xu, Chao Yang
• Keywords: Fault Diameter, IPL 2007, K-connected Graph, Maximum Diameter