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Bi-Squashing Ssub.2,2-Designs into -Designs
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Journal Article
Bi-Squashing Ssub.2,2-Designs into -Designs
2024
Overview
A double-star S[sub.q1,q2] is the graph consisting of the union of two stars, K[sub.1,q1] and K[sub.1,q2] , together with an edge joining their centers. The spectrum for S[sub.q1,q2] -designs, i.e., the set of all the n∈N such that an S[sub.q1,q2] -design of the order n exists, is well-known when q[sub.1] =q[sub.2] =2. In this article, S[sub.2,2] -designs satisfying additional properties are investigated. We determine the spectrum for S[sub.2,2] -designs that can be transformed into (K[sub.4] −e)-designs by a double squash (bi-squash) passing through middle designs whose blocks are copies of a bull (the graph consisting of a triangle and two pendant edges). Here, the use of the difference method enables obtaining cyclic decompositions and determining the spectrum for cyclic S[sub.2,2] -designs that can be purely bi-squashed into cyclic (K[sub.4] −e)-designs (the middle bull designs are also cyclic).
Publisher
MDPI AG
Subject
