Abstract

AbstractWe answer a question on group connectivity suggested by Jaeger et al [J. Combin. Theory, Ser. B 56 (1992), pp. 165–182]: we find that ‐connectivity does not imply ‐connectivity, neither vice versa. We use a computer to find the graphs certifying this and to verify their properties using a nontrivial enumerative algorithm (and we also use an independent implementation of a straightforward algorithm to double‐check our results). We provide a simple construction to provide an infinite family of examples. While the graphs we found are small (the largest has 15 vertices and 21 edges), a computer‐free approach remains elusive.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.