This work determines the maximum atom bond sum connectivity index in unicyclic graphs with perfect matching, indicating the corresponding extremal graphs.
The atom bond sum connectivity (ABS) index of a graph Γ = (V(Γ), E(Γ)) is formulated by ABS(Γ) = ∑xy ∈ E(Γ) √{{dΓ(x) + dΓ(y) - 2}{dΓ(x) + dΓ(y)}}, where dΓ(x) denotes the degree of vertex x in Γ. In this work, we determine the maximum value of atom bond sum connectivity index of chemical unicyclic graphs with a perfect matching and identify the corresponding extremal graphs. Our discoveries extend the results of the recent paper [Wang et al., MATCH Commun. Math. Comput. Chem. 92 (2024) 653-669] from chemical trees with a perfect matching to chemical unicyclic graphs with a perfect matching.
No takes yet. Share an insight, caveat, or question.
Du et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: