The Randić index R(G) of a nontrivial connected graph G is defined as the sum of the weights (d(u)d(v))− 1 2 over all edges e = uv ofG. We prove that R(G) ≥ d(G)/2, where d(G) is the diameter of G. This immediately implies that R(G) ≥ r(G)/2, which is the closest result to the well-known Grafiti conjecture R(G) ≥ r(G) − 1 of Fajtlowicz [4], where r(G) is the radius of G. Asymptotically, our res...

The eccentricity connectivity index of a molecular graph G is defined as (G) = aV(G) deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to other vertices of G and deg(a) is degree of vertex a. Here, we compute this topological index for some infinite classes of dendrimer graphs.

The atom bond connectivity index of a graph is a new topological index was defined by E. Estrada as ABC(G)  uvE (dG(u) dG(v) 2) / dG(u)dG(v) , where G d ( u ) denotes degree of vertex u. In this paper we present some bounds of this new topological index.

in the recent years, the coherence index is used in many electroencephalographic studies for investigation of brain connectivity in children with adhd disorder. it is suggested that the coherence is a useful index in discrimination of adhd subjects from normal subjects. however, a few studies are accomplished in subtypes of adhd to identify of differences in functional connectivity between adhd...

Background: Ensuring adequate depth of anesthesia during surgery is essential for anesthesiologists to prevent the occurrence of unwanted alertness during surgery or failure to return to consciousness. Since the purpose of using anesthetics is to affect the central nervous system, brain signal processing such as electroencephalography (EEG) can be used to predict different levels of anesthesia....

let g be a graph. in this paper, we study the eccentric connectivity index, the new version ofthe second zagreb index and the forth geometric–arithmetic index.. the basic properties ofthese novel graph descriptors and some inequalities for them are established.

The general sum-connectivity index is a molecular descriptor defined as [Formula: see text], where [Formula: see text] denotes the degree of a vertex [Formula: see text], and α is a real number. Let X be a graph; then let [Formula: see text] be the graph obtained from X by adding a new vertex [Formula: see text] corresponding to each edge of X and joining [Formula: see text] to the end vertices...

in this paper, the degree distance and the gutman index of the corona product of two graphs are determined. using the results obtained, the exact degree distance and gutman index of certain classes of graphs are computed.

let $g$ be a simple connected graph. the edge-wiener index $w_e(g)$ is the sum of all distances between edges in $g$, whereas the hyper edge-wiener index $ww_e(g)$ is defined as {footnotesize $w{w_e}(g) = {frac{1}{2}}{w_e}(g) + {frac{1}{2}} {w_e^{2}}(g)$}, where {footnotesize $ {w_e^{2}}(g)=sumlimits_{left{ {f,g} right}subseteq e(g)} {d_e^2(f,g)}$}. in this paper, we present explicit formula fo...