Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/916345
- Title
- Graphs which are linked cycles
- Author/Creator
-
Adams, Peter;
Eggleton, Roger;
MacDougall, James A.
- Institution
- The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
- Description
- A graph H of order h is an n-linked cycle if it has an induced subgraph G of order g < h and an automorphism α: H → H of order n ≥ 2 such that H = ⋃{αr(G) : 0 ≤ r < n} and G has an induced subgraph K of order k < g such that αr(G) ⋂ αr⁺¹(G) ≅ K for 0 ≤ r < n. Then G is the initial link of this linked cycle, K is its kernel, α|G is the link isomorphism, and any pair (G, α) allowing H to be expressed as a linked cycle yields a generalized factorization of H. For a given standard ordering of all finite graphs, the "earliest" pair (G, α) is a fundamental representation of H. There are 2 593 574 linked cycles among all graphs of order h ≤ 10. The paper gives an overview, and a fundamental representation of each of them is provided on a supporting website.
- Relation
- Congressus Numerantium Vol. 195, p. 75-83
- Relation
- http://utilitasmathematica.org
- Date
- 2009
- Publisher
- Utilitas Mathematica Publishing
- Keyword(s)
-
graph automorphism;
factorization;
linked cycle
- Resource Type
- journal article
- Identifier
- http://hdl.handle.net/1959.13/916345
- Identifier
- ISSN:0384-9864
- Reviewed
20 Visitors
25 Hits
1 Downloads
