Abstract
It is well-known that the maximum exponent that an $n$-by-$n$ boolean primitive circulant matrix can attain is $n-1$. In this paper, we find the maximum exponent attained by $n$-by-$n$ boolean primitive circulant matrices with constant number of nonzero entries in their generating vector. We also give matrices attaining such exponents. Solving this problem we also solve two equivalent problems: 1) find the maximum exponent attained by primitive Cayley digraphs on a cyclic group whose vertices have constant outdegree; 2) determine the maximum order of a basis for ${\Bbb Z}_{n}$ with fixed cardinality.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.