On tricyclic graphs with maximum atom–bond sum–connectivity index

The sum-connectivity, Randić, 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 39Zuo X. Jahanbani A. Shooshtari H. On the atom-bond sum-connectivity index of chemical graphs.J. Mol. Struct. 2024; 1296136849Crossref Scopus (7) Google Scholar) 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.