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- Title
Enumeration of symmetric (45,12,3) designs with nontrivial automorphisms.
- Authors
Crnković, Dean; Danilović, Doris Dumičić; Rukavina, Sanja
- Abstract
We show that there are exactly 4285 symmetric (45,12,3) designs that admit nontrivial automorphisms. Among them there are 1161 self-dual designs and 1562 pairs of mutually dual designs. We describe the full automorphism groups of these designs and analyze their ternary codes. R. Mathon and E. Spence have constructed 1136 symmetric (45,12,3) designs with trivial automorphism group, which means that there are at least 5421 symmetric (45,12,3) designs. Further, we discuss trigeodetic graphs obtained from the symmetric (45; 12; 3) designs. We prove that k-geodetic graphs constructed from mutually non-isomorphic designs are mutually non-isomorphic, hence there are at least 5421 mutually non-isomorphic trigeodetic graphs obtained from symmetric (45; 12; 3) designs.
- Subjects
MATHEMATICAL symmetry; AUTOMORPHISMS; ISOMORPHISM (Mathematics); GRAPH theory; TERNARY codes
- Publication
Journal of Algebra Combinatorics Discrete Structures & Applications, 2017, Vol 4, Issue 3, p145
- ISSN
2148-838X
- Publication type
Article
- DOI
10.13069/jacodesmath.29560