Authors:
Abeer M. Albalahi, Zhibin Du, Akbar Ali, Muhammad Javaid, Amjad E. Hamza
Abstract
This paper gives the optimal values of the sum of a topological index and its reciprocal version of fixed-order
unicyclic graphs for the cases of the first Zagreb index, second Zagreb index, forgotten topological index, and Sombor
index. For each of the aforementioned four topological indices, the cycle graph uniquely attains the minimum value of
the mentioned sum and the graph formed by inserting one edge in the star graph uniquely attains the maximum value of
this sum in the considered class of graphs.
These findings extend the results of the recent paper [W. Gao, MATCH Commun. Math. Comput. Chem. 93 (2025) 535-547]
from trees to unicyclic graphs.
The results about the minimum values remain valid for fixed-order molecular unicyclic graphs.
