English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Cycles have many interesting properties and are widely studied in manydisciplines. In some areas, maximising the counts of $k$-cycles are ofparticular interest. A natural candidate for the construction method used tomaximise the number of subgraphs $H$ in a graph $G$, is the \emph{blow-up}method. Take a graph $G$ on $n$ vertices and a pattern graph $H$ on $k$vertices, such that $n\geq k$, the blow-up method involves an iterative processof replacing vertices in $G$ with a copy of the $k$-vertex graph $H$. In thispaper, we apply the blow-up method on the family of cycles. We then present theexact counts of cycles of length 4 for using this blow-up method on cycles andgeneralised theta graphs.

Exact Counts of $C_{4}$s in Blow-Up Graphs