‎let g=(v,e) be a simple connected graph with vertex set v and edge set e. the first, second and third zagreb indices of g are respectivly defined by: $m_1(g)=sum_{uin v} d(u)^2, hspace {.1 cm} m_2(g)=sum_{uvin e} d(u).d(v)$ and $ m_3(g)=sum_{uvin e}| d(u)-d(v)| $ , where d(u) is the degree of vertex u in g and uv is an edge of g connecting the vertices u and v. recently, the first and second m...

BACKGROUND The pulsatility index (PI) shows continuous blood flow to the end organs and is a significant factor believed to decrease in aortic coarctation. Correction of this factor is of great importance in the treatment of stenotic lesions of the aorta. However, there are minimal data regarding the trend of changes in the PI after stent implantation. Furthermore, the association between the P...

Let $G$ be a finite group and $pi(G)$ be the set of all the prime‎ ‎divisors of $|G|$‎. ‎The prime graph of $G$ is a simple graph‎ ‎$Gamma(G)$ whose vertex set is $pi(G)$ and two distinct vertices‎ ‎$p$ and $q$ are joined by an edge if and only if $G$ has an‎ ‎element of order $pq$‎, ‎and in this case we will write $psim q$‎. ‎The degree of $p$ is the number of vertices adjacent to $p$ and is‎ ...

Valence topological charge-transfer (CT) indices are applied to the calculation of pH at the pI isoelectric point. The combination of CT indices allows the estimation of pI. The model is generalized for molecules with heteroatoms. The ability of the indices for the description of molecular charge distribution is established by comparing them with the pI of 21 amino acids. Linear correlation mod...

let $g$ be a finite group and $pi(g)$ be the set of all the prime‎ ‎divisors of $|g|$‎. ‎the prime graph of $g$ is a simple graph‎ ‎$gamma(g)$ whose vertex set is $pi(g)$ and two distinct vertices‎ ‎$p$ and $q$ are joined by an edge if and only if $g$ has an‎ ‎element of order $pq$‎, ‎and in this case we will write $psim q$‎. ‎the degree of $p$ is the number of vertices adjacent to $p$ and is‎ ...

As in the previous chapter, let us denote points in R by p = (x, y, z) and points in R by u = (u, v). An edge is then defined as the convex hull of (or, equivalently, the line segment between) two distinct points and a triangle as the convex hull of three non-collinear points. We will denote edges and triangles in R with capital letters and those in R with small letters, for example, e = [u1,u2...

The topological index of a graph G is a numeric quantity related to G which is invariant under automorphisms of G. The vertex PI polynomial is defined as v u v e uv PI (G) n (e) n (e). = = + ∑ Then Omega polynomial Ω(G,x) for counting qoc strips in G is defined as Ω(G,x) = ∑cm(G,c)x with m(G,c) being the number of strips of length c. In this paper, a new infinite class of fullerenes is construc...

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and let $d_u$ denote the degree of vertex $u$ in $G$. The Randi'c index of $G$ is defined as${R}(G) =sum_{uvin E(G)} 1/sqrt{d_ud_v}.$In this paper, we investigate the relationships between Randi'cindex and several topological indices.