On the Exponential Atom-Bond Connectivity Index of Graphs

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

Mathematics, 2025, vol. 13, issue 2, 1-19

Abstract: Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological index. The exponential atom-bond connectivity index is defined as follows: e ABC = e ABC ( Υ ) = ∑ v i v j ∈ E ( Υ ) e d i + d j − 2 d i d j , where d i is the degree of the vertex v i in Υ . In this paper, we prove that the double star D S n − 3 , 1 is the second maximal graph with respect to the e ABC index of trees of order n . We give an upper bound on e ABC of unicyclic graphs of order n and characterize the maximal graphs. The graph K 1 ∨ ( P 3 ∪ ( n − 4 ) K 1 ) gives the maximal graph with respect to the e ABC index of bicyclic graphs of order n . We present several relations between e ABC ( Υ ) and A B C ( Υ ) of graph Υ . Finally, we provide a conclusion summarizing our findings and discuss potential directions for future research.

Keywords: graph; atom-bond connectivity index; exponential atom-bond connectivity index; unicyclic graph; bicyclic graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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