On tricyclic graphs with maximum atom-bond sum-connectivity index.

The sum-connectivity, Randic, and atom-bond connectivity indices have a prominent place among those topological indices that depend on the graph's vertex degrees. The ABS (atom-bond sum-connectivity) index is a variant of all the aforementioned three indices, which was recently put forward. Let T ( n ) be the class of all connected tricyclic graphs of order n. Recently, the problem of determining graphs from T ( n ) having the least possible value of the ABS index was solved in (Zuo et al., 2024 [39]) for the case when the maximum degree of the considered graphs does not exceed 4. The present paper addresses the problem of finding graphs from T ( n ) having the largest possible value of the ABS index for n ≥ 5 .