Abstract
Bond (1987) and Bond et al. (1987), conjectured that a quasi-center in an undirected de Bruijn graph UB(d,D) has cardinality at least d−1, and that a quasi-center in an undirected Kautz graph UK(d,D) has cardinality at least d. They proved that for d≥3, the radii of UB(d,D) and UK(d,D) are both equals to D, and conjectured also that the radii of UB(2,D) and UK(2,D) are respectively D−1 and D. In this paper we give results in a more general context which validate these conjectures (excepting that asserting that the radius of UB(2,D) is D−1), and give simplified proofs of the cited results.
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.
