A fundamental component of brain development is the formation of large-scale networks across the cortex. One such network, the default network, undergoes a protracted development, displaying weak connectivity in childhood that strengthens in adolescence and becomes most robust in adulthood. Little is known about the genetic contributions to default network connectivity in adulthood or during de...

Data on Internet performance and the analysis of its trend can be useful for decision makers and scientists alike. Such performance measurements are possible using the PingER methodology. We use the data thus obtained to quantify the difference in performance between developed and developing countries, sometimes referred to as the “digital divide.” Motivated by the recent interest of G8 countri...

Let W1, . . . ,Wn be independent random subsets of [m] = {1, . . . ,m}. Assuming that each Wi is uniformly distributed in the class of d-subsets of [m] we study the uniform random intersection graph Gs(n,m, d) on the vertex set {W1, . . .Wn}, defined by the adjacency relation: Wi ∼ Wj whenever |Wi ∩Wj | ≥ s. We show that as n,m → ∞ the edge density threshold for the property that each vertex of...

Gopalan et al. studied in ICALP06 [17] connectivity properties of the solution-space of Boolean formulas, and investigated complexity issues on the connectivity problems in Schaefer’s framework. A set S of logical relations is Schaefer if all relations in S are either bijunctive, Horn, dual Horn, or affine. They conjectured that the connectivity problem for Schaefer is in P . We disprove their ...

Gopalan et al. studied in ICALP06 [17] connectivity properties of the solution-space of Boolean formulas, and investigated complexity issues on the connectivity problems in Schaefer’s framework. A set S of logical relations is Schaefer if all relations in S are either bijunctive, Horn, dual Horn, or affine. They conjectured that the connectivity problem for Schaefer is in P . We disprove their ...

The generalized k-connectivity of a graph G, denoted by κk(G), is the minimum number internally edge disjoint S-trees for any S⊆V(G) and |S|=k. natural extension classical connectivity plays key role in applications related to modern interconnection networks. burnt pancake BPn godan EAn are two kinds Cayley graphs which posses many desirable properties. In this paper, we investigate 3-connectiv...

For a connected graph G = (V (G), E(G)), a vertex set S ⊆ V (G) is a k-restricted vertex-cut if G − S is disconnected such that every component of G − S has at least k vertices. The k-restricted connectivity κk(G) of the graph G is the cardinality of a minimum k-restricted vertex-cut of G. In this paper, we give the 3-restricted connectivity and the 4-restricted connectivity of the Cartesian pr...

Let H be a graph with a designated vertex s, where edges are weighted by nonnegative reals. Splitting edges e = {u, s} and e′ = {s, v} at s is an operation that reduces the weight of each of e and e′ by a real δ > 0 while increasing the weight of edge {u, v} by δ. It is known that all edges incident to s can be split off while preserving the edge-connectivity of H and that such a complete split...

Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...