PBIB Designs Constructed Through Edges and Paths of Graphs

Gurinder Pal Singh; Davinder Kumar Garg

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P509

PBIB Designs Constructed Through Edges and Paths of Graphs

Gurinder Pal Singh, Davinder Kumar Garg

Citation :

Gurinder Pal Singh, Davinder Kumar Garg, "PBIB Designs Constructed Through Edges and Paths of Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 70-74, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P509

Abstract

In this paper, partially balanced incomplete block (PBIB) designs with two and higher associate classes have been constructed by using edges of incidence vertices and closed paths in various graphs. Forthese formulations, we have considered pentagon graph, pappus graph and Peterson graph for construction offive, three and two associateclassPBIB designsalong with their association schemes respectively. Various kinds of efficiencies of these constructed PBIB designs are also computed for the purpose of comparisons.

Keywords

Partially balanced incomplete block design, path, vertices, edge, pentagon graph, regular graph

References

[1] Anwar Alwardiand N. D Soner“Partially balanced incomplete block designs arising from some minimal dominating sets of SRNT graphs”,InternationalJournal of Mathematical Archive, 2(2), 233-235 (2011).
[2] D.K. Garg and S.A. Farooq“Construction of PBIB designs through chosenlines and triangles of graphs”,InternationalJournal of Mathematics Trends andTechnology,8(1), 25 – 32(2014).
[3] K. Sharma and D.K. Garg “Construction of three associate PBIB designs using some sets of initial blocks”, International Journal of Agricultural and Statistical Sciences (IJASS), 13(1), 55-60 (2017).
[4] P. N. Viney Kumar, D.S. Nandappa,.andU.S. Mahabaleswar “Partially balanced incomplete block design withminimum perfect dominating sets of Clebesch graph”, International Journal of Applied Mathematics and computation,4(1), 39-48 (2012).
[5] S. Shrikol Shailaja, C.GudajeriManjula, and H.G. Shekharappa “Partially balanced incomplete block design arising from minimum total dominating sets in a graph”, International Journal Mathematics Research, 5 (1), 119-126 (2013).
[6] W.H.Clatworthy “Tables of two-associate class partially balanced designs”, NBS Applied-Mathematics, Series 63 (1973).