摘要

To measure the efficiency of a routing in network, Chung et al [The forwarding index of communication networks. IEEE Trans. Inform. Theory, 33 (2) (1987), 224-232] proposed the notion of forwarding index and established an upper bound (n - 1)(n - 2) of this parameter for a connected graph of order n. This note improves this bound as (n - 1)(n 2) - (2n - 2 - Delta [1 + n-1/Delta]) [n-1/Delta], where Delta is the maximum degree of the graph G. This bound is best, possible in the sense that there is a graph G attaining it.