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- W2358498060 abstract "A graph $Gamma$ is called $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of ordered pairs of adjacent vertices. We give a classification of $G$-symmetric graphs $Gamma$ with $V(Gamma)$ admitting a nontrivial $G$-invariant partition $mathcal{B}$ such that there is exactly one edge of $Gamma$ between any two distinct blocks of $mathcal{B}$. This is achieved by giving a classification of $(G, 2)$-point-transitive and $G$-block-transitive designs $mathcal{D}$ together with $G$-orbits $Omega$ on the flag set of $mathcal{D}$ such that $G_{sigma, L}$ is transitive on $L setminus {sigma}$ and $L cap N = {sigma}$ for distinct $(sigma, L), (sigma, N) in Omega$, where $G_{sigma, L}$ is the setwise stabilizer of $L$ in the stabilizer $G_{sigma}$ of $sigma$ in $G$. Along the way we determine all imprimitive blocks of $G_{sigma}$ on $V setminus {sigma}$ for every $2$-transitive group $G$ on a set $V$, where $sigma in V$." @default.
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- W2358498060 date "2016-05-11" @default.
- W2358498060 modified "2023-09-27" @default.
- W2358498060 title "Symmetric spreads of complete graphs" @default.
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