Abstract
Let G be a connected graph of order n. The eccentricity e(v) of a vertex v is the distance from v to a vertex farthest from v. The average eccentricity of G is the mean of all eccentricities in G. We give upper bounds on the average eccentricity of G in terms of order n, minimum degree δ, and girth g. In addition, we construct graphs to show that, if for given g and δ, there exists a Moore graph of minimum degree δ and girth g, then the bounds are asymptotically sharp. Moreover, we show that the bounds can be improved for a graph of large degree Δ.
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.
