On distance-based indices of regular dendrimers using automorphism group action

Abstract

The various topological indices are helpful in predicting the bioactivity of molecular compounds in quantitative structure–activity relationship/quantitative structure–property relationship study. The Balaban index and Harary index are the distance-based indices. The sum-Balaban index is another variant of Balaban index. Harary index can be used to indicate the decay of interaction between any two atoms of molecules. Whereas, the Balaban and sum-Balaban indices can be linked with some physico-chemical properties of octanes and lower benzenoids. In this work, the closed expression of Balaban index, sum-Balaban index, and Harary index of some regular dendrimers in the form of parameter m{\rm{m}} are computed using the action of automorphism group of these dendrimers.

Keywords

• graph automorphism
• balaban index
• sum-balaban index
• regular dendrimer