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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $n,k,t$ be positive integers. What is the maximum number of arcs in adigraph on $n$ vertices in which there are at most $t$ distinct walks of length$k$ with the same endpoints? In this paper, we prove that the maximum number isequal to $n(n-1)/2$ and the extremal digraph are the transitive tournamentswhen $k\ge n-1\ge \max\{2t+1,2\left\lceil \sqrt{2t+9/4}+1/2\right\rceil+3\}$.Based on this result, we may determine the maximum numbers and the extremaldigraphs for $k\ge \max\{2t+1,2\left\lceil \sqrt{2t+9/4}+1/2\right\rceil+3\}$and $n$ is sufficiently large, which generalises the existing results. Aconjecture is also presented.

A note on extremal digraphs containing at most $t$ walks of length $k$ with the same endpoints