Bi-Squashing S 2,2 -Designs into ( K 4 − e )-Designs

Giovanni Lo Faro and Antoinette Tripodi ()
Additional contact information
Giovanni Lo Faro: Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98166 Messina, Italy
Antoinette Tripodi: Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98166 Messina, Italy

Mathematics, 2024, vol. 12, issue 12, 1-8

Abstract: A double-star S q 1 , q 2 is the graph consisting of the union of two stars, K 1 , q 1 and K 1 , q 2 , together with an edge joining their centers. The spectrum for S q 1 , q 2 -designs, i.e., the set of all the n ∈ N such that an S q 1 , q 2 -design of the order n exists, is well-known when q 1 = q 2 = 2 . In this article, S 2 , 2 -designs satisfying additional properties are investigated. We determine the spectrum for S 2 , 2 -designs that can be transformed into ( K 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 2 , 2 -designs that can be purely bi-squashed into cyclic ( K 4 − e ) -designs (the middle bull designs are also cyclic).

Keywords: graph decomposition; double-star; squash (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/12/1879/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/12/1879/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:12:p:1879-:d:1416091

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().