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- W3197236422 abstract "The present paper is devoted classification of $mathrm {AT4}(p,p+2,r)$-graphs. There is a unique $mathrm {AT4}(p,p+2,r)$-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 Gewirtz graph. The existence of an $mathrm {AT4}(p,p+2,r)$-graph with ${p>2}$ remains an open question. It is known that the local graphs of each $mathrm {AT4}(p,p+2,r)$-graph are strongly regular with parameters $big ((p+2)(p^2+4p+2),p(p+3),p-2,pbig )$. In this paper, an upper bound is found for the prime spectrum of the automorphism group of a strongly regular graph with such parameters, and also some restrictions obtained for the prime spectrum and the structure of the automorphism group of an $mathrm {AT4}(p,p+2,r)$-graph in the case when $2<p$ is a prime power. As a corollary, it is shown that there are no arc-transitive $mathrm {AT}(p,p+2,r)$-graphs with $pin {11,17,27}$." @default.
- W3197236422 created "2021-09-13" @default.
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- W3197236422 date "2021-08-31" @default.
- W3197236422 modified "2023-09-27" @default.
- W3197236422 title "The prime spectrum of an automorphism group of an $mathrm {AT4}(p,p+2,r)$-graph" @default.
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- W3197236422 doi "https://doi.org/10.1090/spmj/1677" @default.
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