A local analysis of imprimitive symmetric graphs
Journal of Algebraic Combinatorics, Tome 22 (2005) no. 4, pp. 435-449.
Voir la notice de l'article dans Electronic Library of Mathematics
Summary: Let ? be a $G$-symmetric graph admitting a nontrivial $G$-invariant partition $B {\cal B}$ . Let ? $_{ B}$ _calB be the quotient graph of ? with respect to $B {\cal B}$ . For each block $B \epsilon B {\cal B}$ , 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 ?.
Mots-clés :
keywords symmetric graph, arc-transitive graph, quotient graph, locally quasiprimitive graph
@article{JAC_2005__22_4_a2,
author = {Zhou, Sanming},
title = {A local analysis of imprimitive symmetric graphs},
journal = {Journal of Algebraic Combinatorics},
pages = {435--449},
publisher = {mathdoc},
volume = {22},
number = {4},
year = {2005},
language = {en},
url = {https://geodesic-test.mathdoc.fr/item/JAC_2005__22_4_a2/}
}
Zhou, Sanming. A local analysis of imprimitive symmetric graphs. Journal of Algebraic Combinatorics, Tome 22 (2005) no. 4, pp. 435-449. https://geodesic-test.mathdoc.fr/item/JAC_2005__22_4_a2/