Resolving an Open Problem on the Exponential Arithmetic–Geometric Index of Unicyclic Graphs

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

Mathematics, 2025, vol. 13, issue 9, 1-11

Abstract: Recently, the exponential arithmetic–geometric index ( E A G ) was introduced. The exponential arithmetic–geometric index ( E A G ) of a graph G is defined as E A G ( G ) = ∑ v i v j ∈ E ( G ) e d i + d j 2 d i d j , where d i represents the degree of the vertex v i in G . The characterization of extreme structures in relation to graph invariants from the class of unicyclic graphs is an important problem in discrete mathematics. Cruz et al., 2022 proposed a unified method for finding extremal unicyclic graphs for exponential degree-based graph invariants. However, in the case of E A G , this method is insufficient for generating the maximal unicyclic graph. Consequently, the same article presented an open problem for the investigation of the maximal unicyclic graph with respect to this invariant. This article completely characterizes the maximal unicyclic graph in relation to E A G .

Keywords: extremal graph; exponential arithmetic–geometric index; unicyclic graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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