G-2019-58
Geometric-arithmetic index and minimum degree of connected graphs
Mustapha Aouchiche, Issmail El Hallaoui et Pierre Hansen
In the present paper, we prove lower and upper bounds for each of the ratios \(GA/\delta\)
, as well as a lower bound on \(GA/\sqrt{\delta}\)
, in terms of the order \(n\)
, over the class of connected graphs on \(n\)
vertices, where \(GA\)
and \(\delta\)
denote the geometric-arithmetic index and the minimum degree, respectively. We also characterize the extremal graphs corresponding to each of those bounds. In order to prove our results, we provide a modified statement of a well-known lower bound on the geometric-arithmetic index in terms of minimum degree.
Paru en août 2019 , 11 pages