THE FORWARDING INDEX OF COMMUNICATION-NETWORKS WITH GIVEN CONNECTIVITY

Answering some questions of Heydemann, Meyer, Opatrny and Sotteau [4], we give upper bounds for the forwarding index of graphs of order n and given connectivity k. We first prove that in a k-connected (respectively k-edge connected) graph with n substantially larger than k, the edge-forwarding index of shortest paths is no more than n2/2-(k-1)n+3(k-1)2/8 (respectively [n2/2]-n-2(k-1)2). We next prove that for a k-connected graph the vertex- and edge-forwarding indices are no more than (n-1[(n-k-1)/k] and n[(n-k-1)/k], respectively. Related conjectures are proposed.