On Sum Lordeg index: theory and applications

Abstract

Topological indices are used to understand physicochemical properties of chemical compounds, since they capture some properties of a molecule in a single number. The \emph{sum lordeg index} is defined as
$$
SL(G) = \sum_{u\in V(G)} d_u \sqrt{\log d_u} \,.
$$
The aim of this paper is to obtain new results for the Sum Lordeg Index. We provide some relations between the Sum Lordeg Index and other clasic topological indices. Moreover, we show upper and lower bounds for this topological index on unicyclic graphs and finding the corresponding extremal graphs. Finally, we show that the Sum Lordeg Index is an important tool for predicting the boiling point of cycloalkanes isomers.