In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.

In this paper we present explicit formulas for the eccentric connectivity index of three classes of chain hexagonal cacti. Further, it is shown that the extremal chain hexagonal cacti with respect to the eccentric connectivity index belong to one of the considered types. Some open problems and possible directions of further research are mentioned in the concluding section.

The variable Zagreb (v)M(2) index is introduced and applied to the structure-boiling point modeling of benzenoid hydrocarbons. The linear model obtained (the standard error of estimate for the fit model S(fit)=6.8 degrees C) is much better than the corresponding model based on the original Zagreb M2 index (S(fit)=16.4 degrees C). Surprisingly,the model based on the variable vertex-connectivity ...

Let G be a nontrivial connected graph of order n and k an integer with 2 ≤ k ≤ n. For a set S of k vertices of G, let κ(S) denote the maximum number of edge-disjoint trees T1, T2, . . . , T in G such that V (Ti) ∩ V (Tj) = S for every pair i, j of distinct integers with 1 ≤ i, j ≤ . Chartrand et al. generalized the concept of connectivity as follows. The k-connectivity, denoted by κk(G), of G i...

Let G be a nontrivial connected graph of order n and let k be an integer with 2 ≤ k ≤ n. For a set S of k vertices of G, let κ(S) denote the maximum number l of edge-disjoint trees T1, T2, . . . , Tl in G such that V (Ti)∩V (Tj) = S for every pair i, j of distinct integers with 1 ≤ i, j ≤ l. A collection {T1, T2, . . . , Tl} of trees in G with this property is called an internally disjoint set ...

In Survivable Network problems (a.k.a. Survivable Network Design Problem – SNDP) we are given a graph with costs/weights on edges and/or nodes and prescribed connectivity requirements/demands. Among the subgraphs of G that satisfy the requirements, we seek to find one of minimum cost. Formally, the problem is defined as follows. Given a graph G = (V,E) and Q ⊆ V , the Q-connectivity λQG(uv) of ...

Strong evidence links the 5-HTTLPR genotype to the modulation of amygdala reactivity during fear conditioning, which is considered to convey the increased vulnerability for anxiety disorders in s-allele carriers. In addition to amygdala reactivity, the 5-HTTLPR has been shown to be related to alterations in structural and effective connectivity. The aim of this study was to investigate the effe...

In the vertex connectivity survivable network design problem we are given an undirected graph G = (V,E) and connectivity requirement r(u, v) for each pair of vertices u, v ∈ V .We are also given a cost function on the set of edges. Our goal is to find the minimum cost subset of edges such that for every pair (u, v) of vertices we have r(u, v) vertex disjoint paths in the graph induced by the ch...

The short (S) allele of the serotonin transporter-linked polymorphic region (5-HTTLPR) has been associated with increased susceptibility to depression. Previous neuroimaging studies have consistently showed increased amygdala activity during the presentation of negative stimuli or regulation of negative emotion in the homozygous short allele carriers, suggesting the key role of amygdala respons...

Objective(s): Behavioral and neuroimaging studies have shown that transcranial direct current stimulation, as a non-invasive neuromodulatory technique, beyond regional effects can modify functionally interconnected remote cortical and subcortical areas. In this study, we hypothesized that the induced changes in cortical excitability following the application of cathodal or anodal tDCS over the ...