Partially Balanced Incomplete Block (PBIB)-Designs Arising From Diametral Paths in Graphs

Abstract

A(v,b,r,k,λ_i)-designoverregulargraphG=(V,E)ofdegreedisanorderedpairD=(V,B),where

|V | = v and B, the set of all diametral paths of G, called blocks, containing vertices belonging to the diametral paths, such that two vertices α and β which are i^thassociates occur together in λ_iblocks, the numbers λ_ibeing independent of the choice of the pair α and β. In this paper, we have extended the di- ametraldesignsintroducedbyHuilgoletal.[12]tosomeclassofgraphslike,hypercubeQ_n,thecomplete k-partite graphs, generalized Petersen graphsetc