Suppose Gamma is a group acting on a set X. An r-labeling phi: X to {1, 2, ..., r} of X is distinguishing (with respect to the action of Gamma) if for any sigma in Gamma, sigma not equal id_X, there exists an element x in X such that phi(x) not equal phi(sigma(x)). The distinguishing number, D_{Gamma}(X), of the action of Gamma on X is the minimum r for which there is an r-labeling which is distinguishing. Given a graph G, the distinguishing number of G, D(G),is defined as D(G) = D_{Aut(G)}(V(G)). This thesis determines the distinguishing numbers of all actions of S_5. As a consequence, we
determine all the possible values of the distinguishing numbers of graphs G with Aut(G)=S_5, confirming a conjecture of Albertson and Collins.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0619106-170029 |
| Date | 19 June 2006 |
| Creators | Chiang, Hsiao-wa |
| Contributors | Xuding Zhu, D. J. Guan, T.Wong, L.D. Tong, none |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0619106-170029 |
| Rights | off_campus_withheld, Copyright information available at source archive |
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