Some normal edge-transitive Cayley graphs on Frobenius groups F_(p, 3)
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let G be a finite group and S a subset of G such that S = S^−1and 1_G ∈/ S. Then the Cayley graph Γ = Cay(G, S) relative to S is the graph with vertex set G and edge set E(Γ(G, S)) = {gh | hg^−1 ∈ S}. Since S is inverse closed and does not contain the identity, this graph is undirected and has no loops. A Cayley graph of a finite group G is called normal edge-transitive,if its automorphism group has a subgroup which both normalizes G and acts transitively on edges. In this paper we determine some normal edge-transitive Cayley Graphs on Frobenius Groups F_p,3, where p is a prime and 3 | p − 1.
Abstract
Let G be a finite group and S a subset of G such that S = S^−1and 1_G ∈/ S. Then the Cayley graph Γ = Cay(G, S) relative to S is the graph with vertex set G and edge set E(Γ(G, S)) = {gh | hg^−1 ∈ S}. Since S is inverse closed and does not contain the identity, this graph is undirected and has no loops. A Cayley graph of a finite group G is called normal edge-transitive,if its automorphism group has a subgroup which both normalizes G and acts transitively on edges. In this paper we determine some normal edge-transitive Cayley Graphs on Frobenius Groups F_p,3, where p is a prime and 3 | p − 1.
참고문헌 (5)
- Mehdi Alaeiyan, "Nonnormal Edge-transitive Cubic Cayley Graphs of Dihedral Groups, International Scholarly Research Network ISRN Algebra Volume", 6~ (2011)
- C.E.Praeger, "Finite normal edge-transitive Cayley graphs", Bull.Austral.Math.Soc, 60, pp.207~220 (1999)
- C. Godsil, "Algebraic Graph Theory" (2001), Springer-Verlag
- A.Asghar Talebi, "Some normal edge-transitive Cayley graphs on Dihedral groups", The Journal of Mathematics and Computer Science, 2(3), pp.448~452 (2011)
- Zai-Ping Lu, "On the Normality of Cayley graphs of Order pq", Australaian Journal Of Combinatorics, 27, pp.81~93 (2003)