A NEAR-REGULAR GRAPH DESIGN APPROACH FOR ORDERING THE THREE OPTIMAL (4*4)/4 SEMI-LATIN SQUARES

Title of Publication: A NEAR-REGULAR GRAPH DESIGN APPROACH FOR ORDERING THE THREE OPTIMAL (4*4)/4 SEMI-LATIN SQUARES
Author(s): N.P. UTO, P.E. CHIGBU
Year of Publication: 2010
Abstract
The three optimal (4*4)/4 semi-Latin squares are ordered for experimentation using a near-regular graph design approach. This involves computing the variances of the differences, ij - (i+1)j, in concurrences between ordered pairs of treatments of the squares. An algorithm which shows the steps involved in the computation of these variances is given and a QBASIC program is developed to substantiate the algorithm.  Thus, given the concurrence matrix of a given square, the program executes the steps in the algorithm to generate the required output.  Results show that the square, Ω2, remains the most preferable square for experimentation while the square, Ω1, is preferable to the square, Ω3.
Keywords and Phrases:     Regular-Graph Design, Concurrences, Optimal Design, Quotient Block Design, Trojan Square

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