Non-Cayley-Isomorphic Cayley graphs from non-Cayley-Isomorphic Cayley digraphs
| dc.contributor.author | Morris, Dave W. | |
| dc.contributor.author | Morris, Joy | |
| dc.date.accessioned | 2025-12-11T17:40:19Z | |
| dc.date.available | 2025-12-11T17:40:19Z | |
| dc.date.issued | 2024 | |
| dc.description | Open access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies | |
| dc.description.abstract | A finite group G is said to be a non-DCI group if there exist subsets S1 and S2 of G, such that the associated Cayley digraphs C−→ay(G; S1) and C−→ay(G; S2) are isomorphic, but no automorphism of G carries S1 to S2. Furthermore, G is said to be a non-CI group if the subsets S1 and S2 can be chosen to be closed under inverses, so we have undirected Cayley graphs Cay(G; S1) and Cay(G; S2). We show that if p is a prime number, and the elementary abelian p- group (Zp)r is a non-DCI group, then (Zp)r+3 is a non-CI group. In most cases, we can also show that (Zp)r+2 is a non-CI group. In particular, from Pablo Spiga’s proof that (Z3)8 is a non-DCI group, we conclude that (Z3)10 is a non-CI group. This is the first example of a non-CI elementary abelian 3-group. | |
| dc.identifier.citation | Morris, D. W., & Morris, J. (2024). Non-Cayley-Isomorphic Cayley graphs from non-Cayley-Isomorphic Cayley digraphs. Australasian Journal of Combinatorics, 90(1), 46-59. | |
| dc.identifier.uri | https://hdl.handle.net/10133/7251 | |
| dc.language.iso | en | |
| dc.publisher | Centre for Discrete Mathematics and Computing | |
| dc.publisher.department | Department of Mathematics and Computer Science | |
| dc.publisher.faculty | Arts and Science | |
| dc.publisher.institution | University of Lethbridge | |
| dc.subject | Caley graphs | |
| dc.subject | Elementary abelian groups | |
| dc.subject | CI graphs | |
| dc.subject | CI groups | |
| dc.subject | Isomorphism | |
| dc.title | Non-Cayley-Isomorphic Cayley graphs from non-Cayley-Isomorphic Cayley digraphs | |
| dc.type | Article |