WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
Structures of Fibers of Groups Actions on Graphs
Authors: , , ,
Abstract: In this paper we prove that if G is a group acting on a tree X such that G is fixing no vertex of X, the stabilizers of the edges of X are finite, and the stabilizers $$ G_{v}$$ of the vertices of X act on trees $$X_{v}$$ where $$X_{v} \neq X$$, $$X_{u} \neq X_{v}$$ for all vertices u,v of X, where $$u \neq v$$, nd the stabilizer $$G_{e} $$ of each edge contains no edge x of the tree $$X_{o(x)}$$ such that $$g(x) = \bar{x}$$ for every edge $$g\in G_{x}$$, then there exists a tree denoted $$\tilde{X}$$ and is called the fiber of X such that G acts on $$\tilde{X}$$.