@article {IOPORT.06092215,
    author       = {Li, Xueliang and Shi, Yongtang},
    title        = {On the diameter and inverse degree.},
    year         = {2011},
    journal      = {Ars Combinatoria},
    volume       = {101},
    issn         = {0381-7032},
    pages        = {481-487},
    publisher    = {Charles Babbage Research Centre, Winnipeg, MB},
    abstract     = {The inverse degree of a finite graph $G$ is defined as $r(G)=\sum _{v\in V(G)}\frac {1}{ \deg (v)}$, where deg$(v)$ is the degree of a vertex $v$. {\it P. Erd\H {o}s} et al. [Congr. Numerantium 64, 121--124 (1988; Zbl 0677.05053)] proved that, if $G$ is a connected graph of order $n$, then the diameter of $G$ is less than $(6r(G) + o(1)) \frac {\log n}{\log \log n}$. {\it P. Dankelmann, H. C. Swart} and {\it P. van den Berg} [Discrete Math. 308, No. 5--6, 670--673 (2008; Zbl 1142.05022)] improved this bound by a factor of $2$. The authors of this paper present sharp upper bounds for trees and unicyclic graphs, which improve the results mentioned above if $G$ is a tree.},
    reviewer     = {Tom\'{a}\v{s} Vetr\'{\i}k (Durban)},
    identifier   = {06092215},
}