An arc-colored digraph D is properly (properly-walk) connected if, for any ordered pair of vertices (u,v), the contains a directed path (a walk) from u to v such that arcs adjacent on (on have distinct colors. The proper connection number pc→(D) (the proper-walk wc→(D)) minimum colours make (properly-walk connected). We prove pc→(Cn(S))≤2 every circulant Cn(S) with S⊆{1,…,n−1},|S|≥2 and 1∈S. Fu...

This paper describes a mechanism, called \persis-tent connection," to preserve stream connections after the communicating peer exits and till it restarts. Such connections have many applications: to survive failures that crash one party, network partitions that cut oo the two parties, and temporary disconnection in a mobile computing environment. They can also facilitate suspension of process e...