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

The Kneser graph $K(n, k)$ has as vertices all $k$-element subsets of$[n]=\{1,2,...,n \}$ and an edge between any two vertices that are disjoint. If$n=2k+1$, then $K(n, k)$ is called an odd graph. Let $ n >4$ and $1< k <\frac{n}{2} $. In the present paper, we show that if the Kneser graph $K(n,k)$is of even order where $n$ is an odd integer or both of the integers $n,k $ areeven, then $K(n,k)$ is a vertex-transitive non Cayley graph. Although, theseare special cases of Godsil [8], unlike his proof that uses some very deepgroup-theoretical facts, ours uses no heavy group-theoretic facts. We obtainour results by using some rather elementary facts of number theory and grouptheory. We show that "almost all" odd graphs are of even order, andconsequently are vertex-transitive non Cayley graphs. Finally, we show that if$ k > 4 $ is an even integer such that $k$ is not of the form $ k = 2^t $ forsome $ t> 2 $, then the line graph of the odd graph $O_{k+1}$ is avertex-transitive non Cayley graph.

More odd graph theory from another point of view