A local analysis of imprimitive symmetric graphs

Zhou, Sanming

Journal of Algebraic Combinatorics, Tome 22 (2005) no. 4, pp. 435-449.

Résumé

Summary: Let ? be a $G$-symmetric graph admitting a nontrivial $G$-invariant partition $B\mathcal{B}$ . Let ? ${}_B$ _calB be the quotient graph of ? with respect to $B\mathcal{B}$ . For each block $BϵB\mathcal{B}$ , the setwise stabiliser $G_B$ of $B$ in $G$ induces natural actions on $B$ and on the neighbourhood ? ${}_B$ _calB $(B)$ of $B$ in ? ${}_B$ _calB . Let $G_{(B)}$ and $G_{[B]}$ be respectively the kernels of these actions. In this paper we study certain "local actions" induced by $G_{(B)}$ and $G_{[B]}$, such as the action of $G_{[B]}$ on $B$ and the action of $G_{(B)}$ on ? ${}_B$ _calB $(B)$, and their influence on the structure of ?.

Détail

Mots-clés : keywords symmetric graph, arc-transitive graph, quotient graph, locally quasiprimitive graph