Abstract
The geometric duals of the generalized Petersen graphs G( n, k) are the Greechie representations of the Generalizations of G 32. The duals are denotes by G ∗( n, k) and the generalizations by L( G ∗( n, k)). For these generalizations which are orthomodular posets and lattices, the automorphism groups are completely determined. State properties are also investigated with the following results obtaining. 1. (1) L( G ∗( n, 1)) admits a full set of dispersion free states if n is even. 2. (2) L( G ∗( n, 1)) does not admit a full set of states if n is odd. 3. (3) L( G ∗( n, 2)) admits a full set of dispersion free states for all values of n other than 5 or 8. 4. (4) L( G ∗(8, 2)) admits a full set of states but does not admit a full set of dispersion free states. 5. (5) L( G ∗(5, 2)) does not admit a full set of states. 6. (6) L( G ∗( n, 3)) admits a full set of dispersion free states for all n.
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 callDisclaimer: 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.
