We consider the problem (MSSS) of nding a strongly connected spanning subgraph with the minimum number of arcs in a strongly connected digraph. This problem is NP-hard for general digraphs since it generalizes the hamil-tonian cycle problem. We show that the problem is polynomially solvable for quasi-transitive digraphs. We describe the minimum number of arcs in such a spanning subgraph of a qu...

A fundamental problem in wireless sensor networks is to connect a given set of sensors while minimizing the receiver interference. This is modeled as follows: each sensor node corresponds to a point in R and each transmission range corresponds to a ball. The receiver interference of a sensor node is defined as the number of transmission ranges it lies in. Our goal is to choose transmission radi...

We derive strong structural constraints on the automorphism groups of strongly regular (s. r.) graphs, giving a surprisingly strong answer to a decades-old problem, with tantalizing implications to testing isomorphism of s. r. graphs, and raising new combinatorial challenges. S. r. graphs, while not believed to be Graph Isomorphism (GI) complete, have long been recognized as hard cases for GI, ...