The ever-tightening squeeze of available bandwidth for our telecommunications devices has become a common and persistent problem in the digital age. As the use of cell phones, Wi-Fi and the Internet expand, the capacity of networks and transmission lines to deliver all that information is increasingly strained.

While providers jockey and maneuver for greater bandwidth to service their customers, scientists are busy researching ways to get more out of the networks we have.

A paper by a Massachusetts Institute of Technology student, “A New Perspective on Vertex Connectivity,” delves into the abstract subject of graph theory. Research in the field occupies an important niche, where computer science and mathematics converge.

According to the author, graduate student Mohsen Ghaffari, within graph theory, the concept of edge connectivity—the properties of the connections of lines in a graph—has been well researched and understood. However, he states that the knowledge of vertex connectivity, or the properties of the connections of dots or nodes in a graph, “is much more limited.”

With the help of co-authors Keren Censor-Hillel and Fabian Kuhn, the electrical engineering and computer science student examined the properties of so-called connected dominating sets. These are subsets of nodes or vertices that are connected within the larger graph.

The researchers developed a formula for identifying these subsets within the larger graph. The formula could be a valuable application in the world of telecommunications networking as it can help to determine various possible connections within a network to achieve maximum speed and reliability.