Abstract
A routing R in a graph G is a set of paths { R xy : x, y ϵ V( G)} where, for each ordered pair of vertices ( x, y), R xy links x to y. The load ξ( G, R, x) of a vertex x in the routing R is the number of paths of R for which x is an interior vertex. We define the forwarding diameter μ( G, R) of the pair ( G, R) by μ(G, R)= max x,y ∑ zϵR xy−{x,y} ξ(G,R,Z) and the forwarding diameter μ( G) of G as the minimum of μ( G, R) taken over all possible routings. In this paper, the introduction of the parameter μ( G) is motivated by a natural model of message transmission in networks and we present several properties of μ( G). In particular, we study the value of μ for several families of graphs such as the hypercube and the de Bruijn graphs and we also study the connection of μ( G) with previously introduced transmission parameters.
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