Efficient Regular Graph Generalized Neighbor Designs
Abstract
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 ≤ 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%
respectively.
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References
References
B.L. Misra, B. Das and S.M. Nutan, “Families 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, “On construction of generalized neighbor
designâ€, Sankhya B, vol. 58, pp. 245-253, 1996.
S.N. Mishra, “Families of proper generalized neighbor designsâ€, J. Stat.
Plan. Inference, vol. 137, pp. 1681-1686, 2007.
R.G. Kedia and B.L. Misra, “On 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, “Economical generalized
neighbor designs of use in serologyâ€, Comput. Stat. Data Anal., vol. 53,
pp. 4584-4589, 2009.
M. Akhtar, R. Ahmed and F. Shehzad, “Generalized 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, “Proper generalized neighbor
designs in circular blocksâ€, J. Stat. Plan. Inference, vol. 140, pp. 3498-
, 2010.
F. Shehzad, M.Z. Yab and R. Ahmed, “Some 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,
“Generalized neighbor designs with block size 3â€, J. Stat. Plan.
Inference, vol. 142, pp. 626-632, 2012.
S.A. Cakiroglu, “Optimal regular graph designsâ€, Stat. Comput.,
vol. 28, pp. 103-112, 2018.
I. Iqbal, M.H. Tahir and S.S.A. Ghazali, “Circular neighbor-balanced
designs using cyclic shiftsâ€, Sci. China Math., vol. 52, no. 10, pp. 2243-
, 2009.
K. Hinkelmann, and O. Kempthorne, “Design and Analysis of
Experimentsâ€, John and Wiley & Sons, Inc., Hoboken, New Jersey,
