The Padmakar–Ivan index of a graph G is the sum over all edges uv of G of number of edges which are not equidistant from u and v. In this work, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed. Using this formula, the PI indices of C4 nanotubes and nanotori are computed. c © 2007 Elsevier Ltd. All rights reserved.

Two equal-length strings S and S′ are a parameterized-match (p-match) iff there exists a one-toone function that renames the characters in S to those in S′. Let P be a collection of d patterns of total length n characters that are chosen from an alphabet Σ of cardinality σ. The task is to index P such that we can support the following operations: search(T ): given a text T , report all occurren...

The Sadhana index (Sd) is a newly introduced cyclic index. Efficient formulae for calculating the Sd (Sadhana) index of linear phenylenes are given and a simple relation is established between the Sd index of phenylenes and of the corresponding hexagonal sequences.

OBJECTIVE The purpose of this study was to investigate the aortic isthmus (AoI) flow difference between larger fetus and smaller fetus of twin; and to evaluate the predictive value of early diagnosis of hemodynamic change in twin growth. METHODS This prospective study on 49 pairs of twin fetuses was performed to obtain AoI blood flow data. Cases with structural or chromosomal abnormalities an...

The vertex Padmakar-Ivan (PIv) index of a graph G was introduced as the sum over all edges e = uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper we provide an analogue to the results of T. Mansour and M. Schork [The PI index of bridge and chain graphs, MATCH Commun. Math. Comput. Chem. 61 (2009) 723-734]. Two efficient formulas for calculating th...

BACKGROUND In species across taxa, offspring have means to influence parental investment (PI). PI thus evolves as an interacting phenotype and indirect genetic effects may strongly affect the co-evolutionary dynamics of offspring and parental behaviors. Evolutionary theory focused on explaining how exaggerated offspring solicitation can be understood as resolution of parent-offspring conflict, ...

Since the early 1990s human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) emerged as a global health pandemic, with sub-Saharan Africa the hardest hit. While the successful roll-out of antiretroviral (ARV) therapy provided significant relief to HIV-positive individuals, such treatment can also elicit damaging side-effects. Here especially HIV protease inhibitors (PIs) a...