Abstract: The resistance distance (Kirchhoff index and multiplicative Kirchhoff index) and distance-based (Wiener index and Gutman index) graph invariants of Γ n = P 2 ×K n are considered. Firstly by using the decomposition theorem, we procure the Laplacian and Normalized Laplacian spectrum for graph Γ n , respectively. Based on which, we can procured the formulae for the number of spanning trees and some resistance distance and distance-based graph invariants of graph Γ n . Also, it is very interesting to see that when n tends to infinity, Kf (Γ n ) is a polynomial and W (Γ n ) is a quadratic polynomial.

ABSTRACT GeneXpert is one of the recent technological instruments used to diagnose tuberculosis in a short span of time. In this study, the performance of GeneXpert MTB/RIF assay for the diagnosis of extrapulmonary tuberculosis (EPTB) was compared with light-emitting diode Fluorescent Microscopy (LED-FM) in Khyber Pakhtunkhwa, Pakistan. A total of 737 EPTB samples were collected from tuberculosis (TB) suspected patients. Out of these samples, male to female ratio was 53% (n = 390) to 47% (n = 347) respectively. The sensitivity and specificity was 73% and 100% for GeneXpert, while 40% and 100% for LED-FM microscopy. This shows that the sensitivity of GeneXpert is 40–50%, higher than LED-FM microscopy. GeneXpert also detected low number of bacilli as compared to LED-FM microscopy.