function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...

Resistance to Meloidogyne arenaria race 1 is not currently available in commercial peanut cultivars. Moderate levels of resistance have been identified in Arachis hypogaea plant introductions (PI) in previous greenhouse studies. The purpose of this work was to evaluate the effects of resistance in peanut PI on populations dynamics of M. arenaria in field plots. The PI designated as resistant in...

In this paper the Wiener and hyper Wiener index of two kinds of dendrimer graphs are determined. Using the Wiener index formula, the Szeged, Schultz, PI and Gutman indices of these graphs are also determined.

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...

The PI index is a graph invariant defined as the summation of the sums of edges of neu and nev over all the edges of connected graph G, where neu is the number of edges of G lying closer to u than to v and nev is the number of edges of G lying closer to v than to u. The index is very simple to calculate and has disseminating power similar to that of the Wiener and the Szeged indices. The compre...

Let G be a simple connected graph with the vertex set V = V(G) and the edge set E = E(G), without loops and multiple edges. For counting qoc strips in G, Omega polynomial was introduced by Diudea and was defined as Ω(G,x ) = ( , ). , c c m G c x  where m(G,c) be the number of qoc strips of length c in the graph G. Following Omega polynomial, the Sadhana polynomial was defined by Ashrafi et al ...

Let $A$ and $B$ be two disjoint subsets of the vertex set $V$ of a graph $G$. The set $A$ is said to dominate $B$, denoted by $A rightarrow B$, if for every vertex $u in B$ there exists a vertex $v in A$ such that $uv in E(G)$. For any graph $G$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_p}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i rightarrow V_j$ or $V_j rightarrow...

BACKGROUND In this study, we aimed to investigate the ability of transvaginal Doppler ultrasonography in predicting in vitro fertilization (IVF) outcome in women undergoing this procedure. MATERIALS AND METHODS In this prospective observational study, 65 infertile women underwent IVF procedure in Isfahan, during 2013-2014, were studied. The pulsatility index (PI), resistive index (RI) and pea...