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Title:
On Extremal Graphs with Respect to the Atom-Bond Sum Connectivity Index
Authors:
Swathi Shetty ORCID iD 0009-0002-5607-4191
Billava Ramanna Rakshith ORCID iD 0000-0001-8799-9731
Sayinath Udupa Nagara Vinayaka ORCID iD 0000-0003-3043-9316
Volume
96
Issue
3
Year
2026
Pages
1079-1096
Abstract

Recently, Ali et al. [1] posed several open problems concerning extremal graphs with respect to the atom-bond sum connectivity index. These problems involve characterizing graphs that attain the maximum \( ABS \) index within specific graph classes, including: (i) connected graphs with \( n \) vertices and \( p \) cut-vertices; (ii) connected graphs of order \( n \) with vertex \( k \)-partiteness \( v_k(G) = r \); and (iii) connected bipartite graphs of order \( n \) with a fixed vertex connectivity \( \kappa \). In this paper, we provide complete solutions to all of these problems.