Abstract

In this paper, we have constructed partially balanced incomplete block (PBIB) designs with two and three associate classes by establishing a link between PBIB designs and graphs through the chosen lines and number of triangles. We have considered six configurations for this purpose and constructed four two associate class PBIB designs and two three class PBIB designs.

Keywords

References

[1] H.B Walikar, H.S Ramane, B.D Acharya, H.S Shekhareppa, S.Arumugum, “Partially balanced incomplete block design arising from minimum dominating sets of paths and cycles”, AKCE J. Graphs Combin. 4(2), pp. 223-232(2007).
[2] B Sharada, and N.D Soner ,” Partially Balanced Incomplete Block designs arising from minimum efficient dominating sets of a graphs”, Bull.Pure.Appl.Math.,2(1).pp.47-56(2008)
[3] H.B Wailkar B.D Acharaya, S Shrikol Shailaja, “Designs associated with maximum independent sets of a graph”, Des. Codes. Cryptography., Springer, New york (2009).
[4] P.N. Vinay Kumar and D.Soner Nandappa, “Designs associated with maximum independent sets of cubic graphs”, Journal of computer and Mathematical Science Vol. 1(3), pp.300-309 (2010)
[5] Anwar Alwardi and N.D.Soner,” Partially Balanced Incomplete Block designs arising from some minimal dominating sets of SRNT graphs”, International Journal of Mathematical Archive-2(2), pp.233-235 (2011).
[6] P.N.Vinay Kumar, D.S. Nandappa and U.S. Mahabaleswar, “Partially Balanced incomplete Block design with minimum perfect dominating sets of Clebesch graph”, International Journal of Applied Mathematics and computation Vol.4(1), pp.39-48 (2012).
[7] S.Shrikol Shailaja, C. Gudageri Manjula and H.G.Shekharappa, “Partially balanced incomplete block design arising from minimum total dominating sets in a graph”, International Journal Mathematics Research. Vol.5(1), pp.119-126(2013).