Elsevier

Discrete Mathematics

Volume 310, Issue 4, 28 February 2010, Pages 940-946
Discrete Mathematics

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On diameter and inverse degree of a graph

https://doi.org/10.1016/j.disc.2009.09.014Get rights and content
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Abstract

The inverse degree r(G) of a finite graph G=(V,E) is defined as r(G)=vV1degv, where degv is the degree of vertex v. We establish inequalities concerning the sum of the diameter and the inverse degree of a graph which for the most part are tight. We also find upper bounds on the diameter of a graph in terms of its inverse degree for several important classes of graphs. For these classes, our results improve bounds by Erdős et al. (1988) [5], and by Dankelmann et al. (2008) [4].

Keywords

Diameter
Inverse degree
Chemical graph

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