NOVEL EXTREMAL RESULTS ON THE RANDIC INDEX OF TREES WITH A SPECIFIED TOTAL DOMINATION NUMBER AND IMPLICATIONS IN QSPR MODELING OF ALKANES

NOVEL EXTREMAL RESULTS ON THE RANDIC INDEX OF TREES WITH A SPECIFIED TOTAL DOMINATION NUMBER AND IMPLICATIONS IN QSPR MODELING OF ALKANES

Merin Manuel, Parthiban Angamuthu

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Abstract

The Randi´c index is a fundamental topological invariant in graph theory, extensively explored for its significance, especially within chemical graph theory. It plays a crucial role in characterizing molecular structures and serves as a key tool for analyzing their properties. It is defined as the sum of the reciprocals of the square root of the product of the degrees of the end vertices for each edge in a graph. Understanding extremal properties of this index has considerable significance. This study refines the existing upper bound on the Randi´c index of trees in terms of their order and total domination number and identifies the extremal tree structures corresponding to these parameters. To evaluate the effectiveness of the proposed bound in QSPR studies, an in-depth analysis was conducted to examine its correlation with the physicochemical characteristics of alkanes. Utilizing the QSPR approach, models were developed to predict these properties, producing promising and satisfactory outcomes.

Keywords

Randi´c index, extremal trees, total domination number, QSPR analysis.