Graphs which are linked cycles

Title: Graphs which are linked cycles
Creator: Adams, Peter; Eggleton, Roger; MacDougall, James A.
Relation: Congressus Numerantium Vol. 195, p. 75-83
Relation: http://utilitasmathematica.org
Publisher: Utilitas Mathematica Publishing
Resource Type: journal article
Date: 2009
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.
Subject: graph automorphism; factorization; linked cycle
Identifier: http://hdl.handle.net/1959.13/916345
Identifier: uon:7966
Identifier: ISSN:0384-9864
Language: eng
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