Trees With a Given Independence Number Maximizing the Randić Index

Bojana Borovićanin, Edin Glogić and Emir Zogić

Journal of Applied Mathematics, 2026, vol. 2026, 1-13

Abstract: The Randić index is a classical degree-based descriptor with strong empirical connections to branching-sensitive physicochemical properties of chemical compounds. Defined as RG=∑uv∈EG1/√dudv, for a simple connected graph G, this index has been extensively studied, especially in the context of trees. In this paper we examine the family Fn,α of trees on n vertices with independence number α. We establish the sharp upper bound RT≤gn,α=1/2 n5−√6−√2+2α√6+√2−4−√6+√2+1, with equality if and only if T∈Rn,α (an explicitly described extremal family). Our result determines the exact maximum of the Randić index under a natural sparsity constraint and clarifies how branching interacts with the independence number. Beyond theoretical interest, the bound and the extremal structures provide practical guidance for QSAR/QSPR workflows where R serves as a branching-sensitive descriptor.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:3075657

DOI: 10.1155/jama/3075657

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