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The aim of this pilot study was to determine whether nalbuphine shortens the duration of the active phase during the first stage of labour in pregnant women. Among 1,619 deliveries, we enrolled 302 pregnant women between March 2003 and August 2005. The case group received a nalbuphine injection (n = 57), while the remaining patients served as a control group (n = 245). The effects of nalbuphine on the length of labour were analysed using a survival analysis (log-rank test). The average duration of the initial active phase was 75 and 160 min for the case and control groups, respectively. The reduced duration of the active phase in the case group occurred regardless of oxytocin infusion (p < 0.01) and was without significant risks.

The analysis of networks and graphs through topological descriptors carries out a useful role to derive their underlying topologies. This process has been widely used in biomedicine, cheminformatics, and bioinformatics, where assessments based on graph invariants have been made available for effectively communicating with the various challenging schemes. In the studies of quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs), graph invariants are used to approximate the biological activities and properties of chemical compounds. In this paper, we give the results related to the eccentric-connectivity index, connective eccentricity index, total-eccentricity index, average eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic index, eccentric atom-bond connectivity index, eccentric adjacency index, modified eccentric-connectivity index, eccentric distance sum, Wiener index, Harary index, hyper-Wiener index and degree distance index of a new graph operation named as ''subdivision vertex-edge join'' of three graphs.

The representation of chemical compounds and chemical networks with the M-polynomials is a new idea, and it gives nice and good results of the topological indices. These results are used to correlate the chemical compounds and chemical networks with their chemical properties and bioactivities. In this article, particular attention will be put on the derivation of M-polynomial for the benzene ring embedded in the P-type surface network in 2D. Furthermore, the topological indices based on the degrees are also derived by using the general form of M-polynomial of the benzene ring embedded in the P-type surface network BRm,n. In the end, the graphical representation and comparison of the M-polynomial and the topological indices of the benzene ring embedded in the P-type surface network in 2D are described.