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A set D ⊆ V of a graph G = (V,E) is called a connected power dominating set of G if G[D], the subgraph induced by D, is connected and every vertex in the graph can be observed from D, following the two observation rules for power system monitoring: Rule 1: if v ∈ D, then v can observe itself and all its neighbors, and Rule 2: for an already observed vertex whose all neighbors except one are observed, then the only unobserved neighbor becomes observed as well. Given a graph G, Minimum Connected Power Domination is to find a connected power dominating set of minimum cardinality of G and Decide Connected Power Domination is the decision version of Minimum Connected Power Domination. Decide Connected Power Domination is known to be NP-complete for general graphs. In this paper, we prove that Decide Connected Power Domination remains NP-complete for star-convex bipartite graphs, perfect elimination bipartite graphs and split graphs. This answers some open problems posed in [B. Brimkov, D. Mikesell and L. Smith, Connected power domination in graphs, J. Comb. Optim. 38(1) (2019) 292–315]. On the positive side, we show that Minimum Connected Power Domination is polynomial-time solvable for chain graphs, a proper subclass of perfect elimination bipartite graph, and for threshold graphs, a proper subclass of split graphs. Further, we show that Minimum Connected Power Domination cannot be approximated within (1 − 휖)ln |V | for any 휖 > 0 unless P = NP, for bipartite graphs as well as for chordal graphs. Finally, we show that Minimum Connected Power Domination is APX-hard for bounded degree graphs. [ABSTRACT FROM AUTHOR]

Background: There is dearth of community based nationally representative data on Reproductive tract infections (RTI). Evidence suggests the stigma associated with the symptoms lead to poor health seeking behaviour among women. Objective: To estimate the prevalence and determinants of RTI symptoms among women of reproductive age (WRA) group in a selected rural and urban slum of district Faridabad, Haryana. Methodology: An analytical cross-sectional study was conducted among 15-49 years age group ever married women residing in an urban slum and rural area of Faridabad. Minimum sample size was calculated to be 345. Systematic random sampling was used to interview eligible population using a predesigned structured questionnaire. Outcome variable of interest was at least one symptom of RTI. Prevalence ratio was calculated to identify the association between determinants and outcome. Results: Prevalence of at least one symptom of RTI among the women in urban area was 46.3% and 39.8% in rural area. Condom usage was higher among rural (20.4%) as compared to urban women (13.4%). Women in rural area reported higher proportion of abortions as compared to urban slum (10.2% vs 7.4%). The bivariable analysis revealed that use of sanitary pads, high parity, condom usage by partner and age at marriage as significant association with outcome. When subjected to generalized linear model non usage of condoms by partner (Adj PR (95%CI); 3.31 (1.14-9.57)) remained as an independent determinant of risk of RTI symptoms. Conclusion: Condom usage by partner in this study has emerged out be a protective factor for risk of RTI symptoms. [ABSTRACT FROM AUTHOR]