Broadcasting on Paths, Cycles, and Cliques

Consider a connected graph G = (V,E) with k  ≥ 2 agents situated aat random vertices selected from V. Suppose that one agent is randomly chosen to possess a message. 

At each turn t the agents perform a random walk. An agent in possession of the message passes it to an agent who does not poseess it if they are both located on the same vertex at the end of some round t_o. We are concerned with ∈(G,k), the time it takes for each agent to possess the message. We explore the process for paths, cycles, and cliques.