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 $\Gamma$ be a distance-regular graph with diameter $d$ and Kneser graph$K=\Gamma_d$, the distance-$d$ graph of $\Gamma$. We say that $\Gamma$ ispartially antipodal when $K$ has fewer distinct eigenvalues than $\Gamma$. Inparticular, this is the case of antipodal distance-regular graphs ($K$ withonly two distinct eigenvalues), and the so-called half-antipodaldistance-regular graphs ($K$ with only one negative eigenvalue). We provide acharacterization of partially antipodal distance-regular graphs (among regulargraphs with $d$ distinct eigenvalues) in terms of the spectrum and the meannumber of vertices at maximal distance $d$ from every vertex. This can be seenas a general version of the so-called spectral excess theorem, which allows usto characterize those distance-regular graphs which are half-antipodal,antipodal, bipartite, or with Kneser graph being strongly regular.

The spectral excess theorem for distance-regular graphs having distance-$d$ graph with fewer distinct eigenvalues