### Graph Sampling by Spanning Tree under Stratified Setup

#### Abstract

The sampling theory and its methodologies are based on assumption that the population under survey is of individuals and respondents have provided the answer of questions asked. When population is of graphical structure like containing nodes and edge links then it is complicated to apply the usual sampling procedures. Spanning tree is specified type of a graph, which is always connected with all nodes and becomes a sub-graph. Assume that there are several strata each having structure of graphical population of node-links, each contains graph like spanning tree. A sample containing different size from each stratum is drawn randomly. This paper presents a node-sampling procedure to draw sample and estimate the population mean- edge-length in the setup of stratified graphical structured population of spanning tree. An estimation procedure is suggested and expressions of mean squared error are obtained. Optimum choice of estimator parameter is obtained showing the control over bias as well as mean squared error both. A numerical case in point is given to support of theoretical findings. It is found that node-sampling procedure is worthwhile in stratified population structure.

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