We consider signed graphs, i.e., graphs with positive or negative signs on their edges. The notion of signed strongly regular graph is recently defined by the author (Signed strongly regular graphs, Proceeding of 48th Annual Iranian Mathematical Conference, 2017). We construct some families of signed strongly regular graphs with only two distinct eigenvalues. The construction is based on the well-known method known as star complement technique.

In this paper, we introduce ( p, q)-Bernstein Durrmeyer operators. We define ( p, q)-beta integral and use it to obtain the moments of the operators. We obtain uniform convergence of the operators by using Korovkin's theorem. We estimate direct results of the operators by means of modulus of continuity and Peetre K -functional. Finally, we find Voronovskaya-type theorem for the operators. Mathematics Subject Classification 41A25 · 41A35

In this article, we introduce the q-variant of Beta operator. We find the recurrence formula for mth-order moments. Here, we establish some direct theorems in terms of modulus of continuity for these operators. We also propose conditions for better approximation. In the end, we also propose the Stancu-type generalization. Mathematical Subject Classification: 41A25; 41A35.

In this paper, we introduce Kantorovich type modification of (p, q)-Meyer-König-Zeller operators. We estimate rate of convergence of proposed operators using modulus of continuity and Lipschitz class functions. Further, we obtain the statistical convergence and local approximation results for these operators. In the last section, we estimate the rate of convergence of (p, q)-Meyer-König-Zeller Kantorovich operators by means of Matlab programming.

In this paper, we have proposed an estimator of finite population mean in stratified random sampling. The expressions for the bias and mean square error of the proposed estimator are obtained up to the first order of approximation. It is found that the proposed estimator is more efficient than the traditional mean, ratio, exponential, regression, Shabbir and Gupta (in Commun Stat Theory Method 40:199-212, 2011) and Khan et al. (in Pak J Stat 31:353-362, 2015) estimators. We have utilized four natural and four artificial data sets under stratified random sampling scheme for assessing the performance of all the estimators considered here.