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Open Access Research Article

PBIB-designs with constant block sums arising from different graph parameters

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pp. 2697–2721Vol. 28Issue 7October 2025DOI: 10.47974/JDMSC-2064 Crossmark XML
Received:
08 Nov 2023
Published Online:
15 Sep 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2064
Pages:
2697–2721

Abstract

Khattree introduced the concept of constant block sum partially balanced incomplete block designs (CBS-PBIBDs) in 2019. In this paper, we have tried to extend this concept to designs arising from different graph parameters. We have studied when some graph theoretical parameters such as diametral paths, maximum independent sets and geodetic sets taken as blocks yield CBS-PBIBD for some classes of graphs. We have also given the distance based association schemes for each design and found robustness of these designs using A-, D- and E-optimality criteria. Also we have disproved existence of a (v, β0, μ) design arising from Shrikhande graph proved by Walikar, Acharya and Shirkol by establishing a flaw in their proof and also attempted one of the questions posed by Khattree on CBS-PBIBD.

Keywords

Subject Classifications

Primary 05C1205C5092E10

References

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