Abdullah Al-Husban, Doaa Al-Sharoa, Mohammad Al-Kaseasbeh, R. M. S. Mahmood, "Structures of Fibers of Groups Actions on Graphs," WSEAS Transactions on Mathematics, vol. 21, pp. 650-658, 2022, DOI:10.37394/23206.2022.21.76
Abdullah Al-Husban, Doaa Al-Sharoa, Mohammad Al-Kaseasbeh, R. M. S. Mahmood. Structures of Fibers of Groups Actions on Graphs.
WSEAS Transactions on Mathematics. 2022;21:650-658. 10.37394/23206.2022.21.76
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 $$\tilde{X}$$.
Keywords:
Actions on trees with inversions, trees, groups acting on trees, stabilizers, orbits, and the orbit space
Pages: 650-658 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 21, 2022, Art. #76 DOI: 10.37394/23206.2022.21.76
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