On chemical and mathematical characteristics of generalized degree–based molecular descriptors

This paper deals with the properties of the generalized Gutman–Milovanović index, generalized elliptic–Sombor index, generalized Zagreb–Sombor index, and general Euler–Sombor index. These include, as special cases, several previously studied molecular descriptors and most of their general versions; for instance, the general Randić index, the general sum-connectivity index, the general Sombor index, etc. The aforementioned descriptors are examined for their applicability in predicting 13 properties of octane isomers, and the results are compared with the ones generated by a benchmark data set (proposed by the International Academy of Mathematical Chemistry), containing 102 descriptors of octane isomers, and also with variable and discrete Adriatic indices. Although these descriptors slightly outperform the descriptors considered for comparison in several cases, a considerable improvement is detected in the case of boiling point. Several fundamental bounds and optimal results of the above-said descriptors are also reported.