Let $c_n$ denote the number of vertex-labeled connected graphs on $n$ vertices. Using group actions and elementary number theory, we show that the infinite sequence, $c_n : n \ge 1,$ is ultimately periodic modulo every positive integer. We state and prove our results for sequences defined by a weighted generalization of $c_n$ and conjecture that these results are suggestive of similar periodic behavior of the Tutte polynomial evaluations of the complete graph $K_n$ at integer points.

This paper addresses the problem of reliably multicasting Web resources across wireless local area networks (WLANs) in support of collaborative computing applications. An adaptive forward error correction (FEC) protocol is described, which adjusts the level of redundancy in the data stream in response to packet loss conditions. The proposed protocol is intended for use on a proxy server that supports mobile users on a WLAN. The software architecture of the proxy service and the operation of the adaptive FEC protocol are described. The performance of the protocol is evaluated using both experimentation on a mobile computing testbed as well as simulation. The results of the performance study show that the protocol can quickly accommodate worsening channel characteristics in order to reduce delay and increase throughput for reliable multicast channels.