Online graph exploration often requires one of the exploring agents to visit each vertex. The authors define and analyze such exploration for an undirected graph in the least numbers of steps for a multi-collaborating-agent scenario. The problem has been modeled as the traveling salesmen problem of operations research. Also, the authors consider the issue of communication between the agents, calling their problem tree exploration with global communications (TEG). The paper suggests a mathematical procedure to solve TEG. This very formal analytical study revolves around a set of mathematical entities (procedures, definitions, lemma, and theorems) and their definitions, and proof as applicable. The paper claims that the procedure/strategy gives results in finite numbers of steps within calculable bounds in an environment where agents can exchange information completely.

The paper lists 22 references. It would interest researchers in applied mathematics and information science.