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Mean Edge Estimation in Population of Planar Graph Using Stratified Sampling Procedure

Deepika Rajoriya, Diwakar Shukla, Shashikant Trivedi, Sharad Pathak


When stratified sampling is used then the population has the capacity to be grouped on the
basis of certain characteristics. Generally in survey sampling the respondents are individual
persons and they are physically unlinked. Consider a situation of graphical structure where
nodes and edges are the main constituents and if somebody wants to estimate the average
length of edges between two nodes then it is a problem under usual sampling setup. This
paper assumes the planner graph situation in each strata and attempt has been made to
estimate the average edge length between any two nodes of planner graph based stratified
population. A node sampling procedure is developed for drawing a sample using matrices. An
estimator has been suggested for estimating the mean edge length parameter. It is found that
the suggested methodology has optimal properties and found efficient also.
AMS Subject Classification: 62D99, 62–07 and 62–09.

Keywords: Planar graph, Stratified sampling and Node sampling procedure

Cite this Article Diwakar Shukla, Shashikant Trivedi, Sharad Pathak, Deepika Rajoriya. Mean Edge Estimation in Population of Planar Graph Using Stratified Sampling Procedure. Research & Reviews: Journal of Statistics. 2019; 8(3): 11–31p.


plaar graph, stratified sampling and Node sampling procedure

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Aleksandrov, L., Djidjev, H., Guo, H. and Maheshwari, A. (2007): Regular Papers: Partitioning planar graphs with costs and weights, Journal of Experimental Algorithmics (JEA), 11, 45-55.

Frederickson, G. N. (1988): Planar graph decomposition and all pairs shortest paths, Journal of the ACM (JACM), 162-204.

Gazit, H. and Reif J. (1990): A randomized parallel algorithm for planar graph isomorphism, Proceedings of the 2nd Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA '90), 210-219.

Grigni, M., Koutsoupias E. and Papadimitriou C. (1995): An approximation scheme for planar graph TSP, 36th Annual Symposium on Foundations of Computer Science (FOCS'95), 640-648.

Osthus, D., Promel, H. J. and Taraz, A. (2003): On random planar graphs, the number of planar graphs and their triangulations, Journal of Combinatorial Theory (B), 88, 119-134.

Parson, T. D. (1971): On Planar Graphs, Am. Math. Monthly, 78 No. 2, 176-178.

Shih, W. K., Wu S. and Kuo, Y. S. (1990): Unifying maximum cut and minimum cut of a planar graph, IEEE Transactions on Computers, 694-697.

Shukla, D., Singh, V. K. and Singh, G. N. and (1991): On the use of transformation in factor type estimator, METRON (1991), vol. 49, 1-4, 349-361.

Shukla, D. (2002): F-T Estimator under two-phase sampling, Metron, 60,1-2, 97-106.

Shukla, D. and Rajput, Y.S. and Thakur, N. S. (2009): Estimation of spanning tree mean-edge using node sampling, Model Assisted Statistics and Applications, 4, 23-37.

Shukla, D. and Rajput, Y.S. and Thakur, N. S. (2010): Edge Estimation in population of planer graph using sampling, Journal of Reliability and Statistical Studies, 3, 13-29.

Shukla, D., Rajput, Y. S. and Thakur, N. S. (2014): Edge Estimation in the Population of a Binary Tree Using Node-Sampling, Communication in Statistics- Theory and Methods, 43, 13, 2815-2829.

Singh, V. K. and Shukla, D. (1987): One parameter family of Factor-Type ratio estimator, Metron, 45, 1-2, 273-283.

Singh, V. K. and Shukla, D. (1993): An efficient one parameter family of Factor-Type estimators in sample Surveys, Metron, 51, 1-2, 139-159.

Singh, D. and Choudhary, F. S. (1986): Theory and Analysis of Sample Survey Design, Wiley Eastern Limited, New Delhi.

Sukhatme, P. V., Sukhatme, B. V., Sukhatme, S. and Ashok, C. (1984): Sampling Theory of Surveys with Applications, Iowa State University Press, I.S.A.S. Publication, New Delhi.



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