We introduce a partial order on the collection of chemical trees based on tree transformations. This partial order is tightly related to the Randić connectivity index χ. Its analysis provides new structural information about the behavior of χ. As an illustration of the approach presented, we give a different and more structural view of some known results about the first values of χ on the colle...

Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.

Anatomical distance has been widely used to predict functional connectivity because of the potential relationship between structural connectivity and functional connectivity. The basic implicit assumption of this method is "distance penalization." But studies have shown that one-parameter model (anatomical distance) cannot account for the small-worldness, modularity, and degree distribution of ...

Introduction: Long-term stressful situations can drastically influence one’s mental life. However, the effect of mental stress on recognition of emotional stimuli needs to be explored. In this study, recognition of emotional stimuli in a stressful situation was investigated. Four emotional conditions, including positive and negative states in both low and high levels of arousal were analy...

Three sets of flavonoid derivatives (N=32, 40, and 74) and logarithms of their dissociation constants (log Kd) that describe flavonoid affinity toward P-glycoprotein were modelled using six connectivity indices. The best results were obtained with the zero-order valence molecular connectivity index (0χv) for all three sets. Standard errors of the calibration models were around 0.3, and of the c...

The sum-connectivity index R′(G) of a graph G is the sum of the weights (du +dv) − 2 of all edges uv of G, where du and dv are the degrees of the vertices u and v in G. This index was recently introduced in [B. Zhou, N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46(2009), 1252–1270]. In this paper, we give the sharp lower bound of the sum-connectivity index of n-vertex unicyclic ...

On the African continent, Morocco is considered among most connected countries, according to liner shipping connectivity index. Since optimal can reduce CO2 emissions and trade costs, through this paper we aimed deepen understanding of maritime based on bilateral index 138 its economic partners. We first established an overview evolution in highlighted main regional partners, then defined a sta...

Dvořák et al. introduced a variant of the Randić index of a graph G, denoted by R′(G), where R′(G) = ∑ uv∈E(G) 1 max{d(u),d(v)} , and d(u) denotes the degree of a vertex u in G. The coloring number col(G) of a graph G is the smallest number k for which there exists a linear ordering of the vertices of G such that each vertex is preceded by fewer than k of its neighbors. It is well-known that χ(...