Construction of neighbor designs of block size 4 for all values of v ≥ 5 by using the method of addition

ABSTRACT

In this article, a general method of construction of neighbor block designs is given. The designs are constructed using variation of a simple method which we refer to as the method of addition (renamed as the method of cyclic shifts). We give complete solution of neighbor balanced designs for k = 4 for any value of v. We also give many series of generalized neighbor designs (GNDs). In the last section, we have constructed GNDs in a sequential manner (as Did John 1981) for v ≤ 50 and r is multiple of k.

KEYWORDS:

• Generalized neighbor balanced block design
• Method of addition
• Neighbor balanced block designs
• Regular graph design
• Sequential design.

MATHEMATICS SUBJECT CLASSIFICATION:

• 05B05
• 62K10
• 62K99