The Randić index R(G) of a graph G is defined as the sum of 1 √dudv over all edges uv of G, where du and dv are the degrees of vertices u and v, respectively. Let D(G) be the diameter of Gwhen G is connected. Aouchiche et al. (2007) [1] conjectured that among all connected graphs G on n vertices the path Pn achieves the minimum values for both R(G)/D(G) and R(G) − D(G). We prove this conjecture...

for a graph $g$ with edge set $e(g)$, the multiplicative sum zagreb index of $g$ is defined as$pi^*(g)=pi_{uvin e(g)}[d_g(u)+d_g(v)]$, where $d_g(v)$ is the degree of vertex $v$ in $g$.in this paper, we first introduce some graph transformations that decreasethis index. in application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum zagreb ...

Introduction: Ensuring an adequate Depth of Anesthesia (DOA) during surgery is essential for anesthesiologists. Since the effect of anesthetic drugs is on the central nervous system, brain signals such as Electroencephalogram (EEG) can be used for DOA estimation. Anesthesia can interfere among brain regions, so the relationship among different areas can be a key factor in the anesthetic process...

Let G be a graph. In this paper, we study the eccentric connectivity index, the new version of the second Zagreb index and the forth geometric–arithmetic index.. The basic properties of these novel graph descriptors and some inequalities for them are established.

To obtain evidence linking long-term potentiation (LTP) and memory, we examined whether LTP induction modifies functional relationship among neurons in the rat hippocampus. In contrast to neurons in low-frequency stimulated or AP5-treated slices, LTP induction altered 'functional connectivity,' as defined by the degree of synchronous firing, among simultaneously recorded neurons in the CA3 regi...

Abstract In this note, we show a sharp lower bound of $$\min \left\{{\sum\nolimits_{i = 1}^k {{d_G}({u_i}):{u_1}{u_2} \ldots {u_k}}} \right.$$ min { ∑ i = 1 k </mml:msubs...

Many existing degree based topological indices can be clasified as bond incident degree (BID) indices, whose general form is BID(G) = ∑ uv∈E(G) Ψ(du, dv), where uv is the edge connecting the vertices u, v of the graph G, E(G) is the edge set of G, du is the degree of the vertex u and Ψ is a non-negative real valued (symmetric) function of du and dv. Here, it has been proven that if the extensio...