Compatible Factorization and Triad Design for Complete Graph of Some Orders رسالة ماجستير

Abstract

Triad design TD)») for some orders , where w = Gn + 5 These are methods of arranging distinct triples (listing and counting triangles) on objects with some properties. Previ- ous studies on TD(v) reported its existence when w = 6n + 1 and = 6n + 5 and TD(7) were developed by using a brute-force method. Furthermore, a starter of triad design, STD(v( = SCF)v) SCFtw). Additionally, in this thesis, new technique for STD(u) algorithms, known as the ”Generalized Interval Method - GIM constructed, by analyzing the pattern of the triples by illustrating the cases = 5, 11, 17, 23 and 29. At the end, this technique, lists lhe element of TD(6n + 5( by repeated addition of l )mod o( from the S7T'D)).

We focus on the construction of triad design for complete graph Ky. We construct a new method for developing a triad design on objects TD(v) that counts and list all triangles in K,. This method depends on analyzing the triples

to construct the starter. We illustrate the method by considering the cases =

11, 17, 23 and 29 Then we conclude the general case of = Gn + 5. We illustrate our results by building TD(11(, TD)17( and TD)23) .