The Minimal Molecular Tree for the Exponential Randić Index

Jayanta Bera and Kinkar Chandra Das ()
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Jayanta Bera: Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea
Kinkar Chandra Das: Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea

Mathematics, 2024, vol. 12, issue 22, 1-20

Abstract: Topological indices are numerical parameters that provide a way to quantify the structural features of molecules using their graph representations. In chemical graph theory, these indices have been effectively employed to predict various physico-chemical properties of molecules. Among these, the Randić index stands out as a classical and widely used molecular descriptor in chemistry and pharmacology. The Randić index R ( G ) for a given graph G is defined as R ( G ) = ∑ v i v j ∈ E ( G ) 1 d ( v i ) d ( v j ) , where d ( v i ) represents the degree of vertex v i and E ( G ) is the set of edges in the graph G . Given the Randić index’s strong discrimination ability in describing molecular structures, a variant known as the exponential Randić index was recently introduced. The exponential Randić index E R ( G ) for a graph G is defined as E R ( G ) = ∑ v i v j ∈ E ( G ) e 1 d ( v i ) d ( v j ) . This paper further explores and fully characterizes the minimal molecular trees in relation to the exponential Randić index. Moreover, the chemical relevance of the exponential Randić index is also investigated.

Keywords: molecular tree; exponential Randi? index; extremal graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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