We define a near-automorphism a of a Latin square L to be an isomorphism such that L and aL differ only within a 2Γ2 subsquare. We prove that for all n β₯ 2 except n β{3, 4}, there exists a Latin square which exhibits a near-automorphism. We also show that if a has the cycle structure (2, n-2), then
Automorphism free latin square graphs
β Scribed by K.T. Phelps
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 837 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
In this paper, we show that there exists an automorphism free latin square graph of order n for all n a 7 and that the number of such graphs goes to infinity with n. These results are then applied to the construction of automorphism free Steiner triple systems.
π SIMILAR VOLUMES
## Abstract An orthogonal latin square graph (OLSG) is one in which the vertices are latin squares of the same order and on the same symbols, and two vertices are adjacent if and only if the latin squares are orthogonal. If __G__ is an arbitrary finite graph, we say that __G__ is realizable as an O
By a square in an undirected graph β« , we mean a cycle x , y , z , w such that x is not adjacent to z and y is not adjacent to w . Suppose that β« is a strongly regular graph with Ο 2 , and assume that β« does not contain a square . Pick any vertex x of β« and let β« Π denote the induced subgraph on the