Abstract
By means of the variable neighborhood search algorithm, a newly designed heuristic approach to combinatorial optimization, we established the structure of the chemical trees possessing extremal (maximal and minimal) values for the Randić connectivity index ( χ). These findings were eventually corroborated by rigorous mathematical proofs. As could have been anticipated, the n-vertex tree with maximum χ is the path. The n-vertex chemical tree with minimum χ-value is not unique. The structures of such chemical trees (which should be considered as the graph representations of the most branched alkanes) are fully characterized.
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