Abstract
The k -diameter of a graph Γ is the largest pairwise minimum distance of a set ofk vertices in Γ, i.e., the best possible distance of a code of size k in Γ. Ak -diameter for some k is called a multidiameter of the graph. We study the function N(k,Δ , D), the largest size of a graph of degree at most Δ and k -diameter D. The graphical analogues of the Gilbert bound and the Hamming bound in coding theory are derived. Constructions of large graphs with given degree and k -diameter are given. Eigenvalue upper bounds are obtained. By combining sphere packing arguments and eigenvalue bounds, new lower bounds on spectral multiplicity are derived. A bound on the error coefficient of a binary code is given.
Sign-in/Register to access full text options 
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.
