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

In this work, we study a mathematically rigorous metric of a graphvisualization quality under conditions that relate to visualizing a bipartitegraph. Namely we study rectilinear crossing number in a special arrangement ofthe complete bipartite graph where the two parts are placed on two concentriccircles. For this purpose, we introduce a combinatorial formulation to countthe number of crossings. We prove a proposition about the rectilinear crossingnumber of the complete bipartite graph. Then, we introduce a geometricoptimization problem whose solution gives the optimum radii ratio in the casethat the number of crossings for them is minimized. Later on, we study themagnitude of change in the number of crossings upon change in the radii of thecircles. In this part, we present and prove a lemma on bounding the changes inthe number of crossings of that is followed by a theorem on asymptotics of thebounds.

Rectilinear crossing number of the double circular complete bipartite graph