Some Properties of Cayley Graphs on Symmetric Groups S_n

Adiga, Chandrashekar and Ariamanesh, Haidar (2012) Some Properties of Cayley Graphs on Symmetric Groups S_n. International Journal of Algebra, 6 (17-20). pp. 807-813. ISSN 1312-8868

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Let G be a finite group and S a subset of G such that S = S-1 and 1G /. S. Then the Cayley graph G = Cay(G,S) relative to S is the graph with vertex set G and edge set E(G(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 nonempty subset S of G is called a Cayley subset if S = S-1 and 1G /. S. In this paper we determine the number of Cayley graphs on Symmetric group Sn and Alternating group An that are undirected. We also show that up to isomorphism there are exactly 8 Cayley graphs of S3 and 4 Cayley graphs of S4 of valency 2.

Item Type: Article
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: C Swapna Library Assistant
Date Deposited: 28 Aug 2019 09:28
Last Modified: 08 Jul 2022 11:04

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