The ability of a robot team to reconfigure itself is useful in many applications: for metamorphic robots to change shape, for swarm motion towards a goal, for biological systems to avoid predators, or for mobile buoys to clean up oil spills. Inmany situations, auxiliary constraints, such as connectivity between team members or limits on the maximum hop-count, must be satisfied during reconfigur...

In theoretical chemistry, -modified Wiener index is a graph invariant topological index to analyze the chemical properties of molecular structure. In this note, we determine the minimum -modified Wiener index of graph with fixed connectivity or edge-connectivity. Our results also present the sufficient and necessary condition for reaching the lower bound.

In many applications it is necessary to have some guarantees on the coverage, connectivity and lifetime of the Wireless Sensor Networks(WSN). Coverage problem is regarding how to ensure that each of the points in the region to be monitored is covered by the sensors. In maximizing coverage, the sensors need to be placed not too close to each other so that the sensing capability of the network is...

Brain function is often characterized by the connections and interactions between highly interconnected brain regions. Pathological disruptions in these networks often result in brain dysfunction, which manifests as brain disease. Typical analysis investigates disruptions in network connectivity based correlations between large brain regions. To obtain a more detailed description of disruptions...

We show that Maximum Independent Set on connected graphs of average degree at most three can be solved in O(1.08537) time and linear space. This improves previous results on graphs of maximum degree three, as our connectivity requirement only functions to ensure that each connected component has average degree at most three. We link this result to exact algorithms of Maximum Independent Set on ...

For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components and a minimum vertex separator is a vertex separator of least cardinality. The vertex connectivity refers to the size of a minimum vertex separator. For a connected graph G with vertex connectivity k (k ≥ 1), the connectivity augmentation refers to a set S of edges whose augmentation toG...

the first extended zeroth-order connectivity index of a graph   g is defined as 0 1/2 1 ( ) ( ) ,   v   v v g      g d      where   v   (g) is the vertex set of g, and v d is the sum of degrees of neighbors of vertex v in g. we give a sharp lower bound for the first extended zeroth-order connectivity index of trees with given numbers of vertices and pendant vertices,...