Optimization problems for variable Randic type lodeg index and other indices

A large number of graph invariants are studied in mathematical chemistry. Among them the variable Randic type lodeg index RLIa was found to have applicative properties. The aim of this paper is to obtain
new inequalities for the variable Randic type lodeg index, and to characterize graphs extremal with respect to them. In particular, some of the open problems posed by Vukicevic are solved in this paper; we characterize graphs with maximum and minimum values of the RLIa index, for every a > 0, in the following sets of graphs with n vertices: graphs, connected graphs, graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, our results can be applied to a large class of topological indices, as variable sum lodeg index and variable inverse sum lodeg index, solving some of the open problems posed by Vukicevic.

Optimization problems for variable Randic type lodeg index and other indices Articles