Efficient Regular Graph Generalized Neighbor Designs
In this study we have constructed a class of economical block designs called regular graph generalized
neighbor designs for circular blocks of size 4 and v â‰¤ 50. This class of design can provide an efficient
alternative of universally optimal neighbor designs. These designs will increase the applications of
regular graph designs particularly in the fields of serology, agro forestry and agriculture, etc. In terms
of efficiency factor, proposed designs are more efficient as compared with other generalized neighbor
designs. The two best designs, for v =26 and v =50, have percentage of upper bound 99.91% and 99.93%
B.L. Misra, B. Das and S.M. Nutan, â€œFamilies of neighbor designs and
their analysesâ€, Commun. Stat. Simul. Comput., vol. 20, no. 2 and 3,
pp. 427-436, 1991.
N.K. Chaure and B.L. Misra, â€œOn construction of generalized neighbor
designâ€, Sankhya B, vol. 58, pp. 245-253, 1996.
S.N. Mishra, â€œFamilies of proper generalized neighbor designsâ€, J. Stat.
Plan. Inference, vol. 137, pp. 1681-1686, 2007.
R.G. Kedia and B.L. Misra, â€œOn construction of generalized neighbor
design of use in serologyâ€, Stat Probab Lett., vol. 18, pp. 254-256, 2008.
R. Ahmed, M. Akhtar and M.H. Tahir, â€œEconomical generalized
neighbor designs of use in serologyâ€, Comput. Stat. Data Anal., vol. 53,
pp. 4584-4589, 2009.
M. Akhtar, R. Ahmed and F. Shehzad, â€œGeneralized neighbor designs
in circular blocksâ€, World Appl. Sci. J., vol. 8, no. 2, pp. 161-166, 2010.
M.Z. Yab, F. Shehzad and R. Ahmed, â€œProper generalized neighbor
designs in circular blocksâ€, J. Stat. Plan. Inference, vol. 140, pp. 3498-
F. Shehzad, M.Z. Yab and R. Ahmed, â€œSome series of proper
generalized neighbor designsâ€, J. Stat. Plan. Inference, vol. 141,
pp. 3808-3813, 2011.
I. Iqbal, M.H. Tahir, M.L. Aggarwal, A. Asghar and I. Ahmed,
â€œGeneralized neighbor designs with block size 3â€, J. Stat. Plan.
Inference, vol. 142, pp. 626-632, 2012.
S.A. Cakiroglu, â€œOptimal regular graph designsâ€, Stat. Comput.,
vol. 28, pp. 103-112, 2018.
I. Iqbal, M.H. Tahir and S.S.A. Ghazali, â€œCircular neighbor-balanced
designs using cyclic shiftsâ€, Sci. China Math., vol. 52, no. 10, pp. 2243-
K. Hinkelmann, and O. Kempthorne, â€œDesign and Analysis of
Experimentsâ€, John and Wiley & Sons, Inc., Hoboken, New Jersey,