Exploration of Cube Shape from Hypercube Graph Partially Balanced Incomplete Block Designs: A Vertex Approach

This article explored Cube shape from Hypercube graph Partially Balanced Incomplete Block Designs, PBIBDs, using a Vertex Association Scheme approach. The design is aimed at increases the Efficiency Factor and reduces the Cost of the Experiment. The objects are; design the Hypercube shape, extract Cube from the Hypercube graph and then generate dataset to test the significance of those designs. The hypercube graph gives two interconnected cubes, say, Cube 1 and Cube 2. From the Hypercube graph analysis, the result shows that the blocks are not significance with p-value of 0.4438 > 0.05 and the treatments are significance with the p-value = 0.00001< 0.05. This means that treatment 1 and treatment 3 are the outliers. Similarly, Cube 1 analysis shows that the blocks are not significance with p-value = 0.5682 > 0.05 and the treatments are significance with p-value = 0.0048 < 0.05. This means that treatment 1 and treatment 3 are the outliers. But the Cube 2, result shows that both the blocks and the treatments are not significance with p-value of 0.6288 and 0.4354 respectively because there were no outliers in treatment 9 to 16. In conclusion, Cube 1 graph PBIBD is better than the Hypercube graph PBIBD since the Efficiency Factor, E = 0.84 > 0.8229. Also the cost of the experiment is cheaper since bk = 32 < 80. The both graph PBIBD are significance in the data analysis.