The forwarding indices of augmented cubes

For a given connected graph G of order n, a routing R in G is a set of n(n − 1) elementary paths specified for every ordered pair of vertices in G. The vertex (resp. edge) forwarding index of G is the maximum number of paths in R passing through any vertex (resp. edge) in G. Choudum and Sunitha [S.A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2002) 71–84] proposed a variant of the hypercube Qn, called the augmented cube AQn and presented a minimal routing algorithm. This paper determines the vertex and the edge forwarding indices of AQn as 2n/9 + (−1)n+1/9 + n2n/3 − 2n + 1 and 2n−1, respectively, which shows that the above algorithm is optimal in view of maximizing the network capacity. © 2006 Elsevier B.V. All rights reserved.

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Min Xu, Jun-Ming Xu
• Keywords: Connected Graph, Edge, IPL 2007, Ordered Pair