Connectivity κ(G) of a graph G is the minimum number of vertices whose removal leaves the remaining graph disconnected or trivial. This parameter is important for interconnection networks and can be used to measure reliability in such networks. In this paper, a new interconnection network called locally exchanged twisted cube (LETQ for short), denoted LeTQ(s, t), is proposed. We obtain some bas...

The odd edge connectivity of a graph G, denoted by o(G), is the size of a smallest odd edge cut of the graph. Let S be any given surface and be a positive real number. We proved that there is a function fS( ) (depends on the surface S and lim !0 fS( )1⁄41) such that any graph G embedded in S with the odd-edge connectivity at least fS( ) admits a nowhere-zero circular (2þ )-flow. Another major r...

 Mobile sensor networks rely heavily on inter-sensor connectivity for collection of data. Nodes in these networks monitor different regions of an area of interest and collectively present a global overview of some monitored activities or phenomena. A failure of a sensor leads to loss of connectivity and may cause partitioning of the network into disjoint segments. A number of approaches have be...

Introduction: Many theories have been proposed about the etiology of autism. One is related to brain connectivity in patients with autism. Several studies have reported brain connectivity changes in autism disease. This study was performed on Electroencephalogram (EEG) studies that evaluated patients with autism, using functional brain connectivity, and compared them with typically-developing i...

A digraph G = (V, E) with diameter D is said to be s-geodetic, for 1 ≤ s ≤ D, if between any pair of (not necessarily different) vertices x, y ∈ V there is at most one x → y path of length ≤ s. Thus, any loopless digraph is at least 1-geodetic. A similar definition applies for a graph G, but in this case the concept is closely related to its girth g, for then G is s-geodetic with s = b(g − 1)/2...

OBJECTIVE To test whether more physiologically assessed hot flashes were associated with more connectivity in the default mode network (DMN), the network of brain regions active during rest. We particularly focus on DMN networks supporting the hippocampus as this region is rich in estrogen (E) receptors (ER) and has previously been linked to hot flashes. DESIGN Women underwent 24 hours of phy...

Compared to healthy controls, individuals with autism spectrum disorders (ASD) have weaker posterior-anterior connectivity that strengthens less with age within the default network, a set of brain structures connected in the absence of a task and likely involved in social function. The serotonin transporter-linked polymorphic region (5-HTTLPR) genotypes that result in lowered serotonin transpor...