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

This paper is devoted to the problem of classification of ${\rmAT4}(p,p+2,r)$-graphs. There is a unique ${\rm AT4}(p,p+2,r)$-graph with $p=2$,namely, the distance-transitive Soicher graph with intersection array $\{56,45, 16, 1;1, 8, 45, 56\}$, whose local graphs are isomorphic to the Gewirtzgraph. It is still unknown whether an ${\rm AT4}(p,p+2,r)$-graph with $p>2$exists. The local graphs of each ${\rm AT4}(p,p+2,r)$-graph are stronglyregular with parameters $((p+2)(p^2+4p+2),p(p+3),p-2,p)$. In the present paper,we find an upper bound for the prime spectrum of an automorphism group of astrongly regular graph with such parameters, and we also obtain somerestrictions for the prime spectrum and the structure of an automorphism groupof an ${\rm AT4}(p,p+2,r)$-graph in case when $p$ is a prime power. As acorollary, we show that there are no arc-transitive ${\rm AT4}(p,p+2,r)$-graphswith $p\in \{11,17,27\}$.

On the prime spectrum of an automorphism group of an ${\rm AT4}(p,p+2,r)$-graph