- Tytuł:
- Arc-transitive and s-regular Cayley graphs of valency five on Abelian groups
- Autorzy:
- Alaeiyan, Mehdi
- Powiązania:
- https://bibliotekanauki.pl/articles/744001.pdf
- Data publikacji:
- 2006
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Cayley graph
normal Cayley graph
arc-transitive
s-regular Cayley graph - Opis:
- Let G be a finite group, and let $1_G ∉ S ⊆ G$. A Cayley di-graph Γ = Cay(G,S) of G relative to S is a di-graph with a vertex set G such that, for x,y ∈ G, the pair (x,y) is an arc if and only if $yx^{-1} ∈ S$. Further, if $S = S^{-1}:= {s^{-1}|s ∈ S}$, then Γ is undirected. Γ is conected if and only if G = ⟨s⟩. A Cayley (di)graph Γ = Cay(G,S) is called normal if the right regular representation of G is a normal subgroup of the automorphism group of Γ. A graph Γ is said to be arc-transitive, if Aut(Γ) is transitive on an arc set. Also, a graph Γ is s-regular if Aut(Γ) acts regularly on the set of s-arcs. In this paper, we first give a complete classification for arc-transitive Cayley graphs of valency five on finite Abelian groups. Moreover, we classify s-regular Cayley graph with valency five on an abelian group for each s ≥ 1.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2006, 26, 3; 359-368
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł