Abstract

Expanding and forwarding are two graphic parameters related to the connectivity and the capacity of the network—the undirected graph with a given routing. Many large networks are composed from some existing smaller networks by using, in terms of graph theory, Cartesian product. The expanding and forwarding parameters of such large networks are associated strongly with that of the corresponding smaller ones. This association also provides a convenient way to determine the two parameters for some known networks such as the hypercube, generalized cube and the mesh, etc. As the generalization of the forwarding index, t-forwarding index is introduced and studied. The study shows that the t-forwarding parameters of a given graph are convergent (refers to the limit t→∞), which reveals some further properties concerning the forwarding parameters of the product graphs.

Author Keywords: Routing; Expanding factor; Forwarding index; Product graph

Mathematical subject codes: 05C90

Article Outline

1. Introduction and definitions

2. Expanding factors

3. Forwarding indices

3.1. Upper bounds and lower bounds

3.2. t-forwarding indices

4. Applications

5. Final remark

References