On extremal graphs with respect to the ABS index
Combinatorics
2025-12-30 v1
Abstract
Recently, Ali et al. posed several open problems concerning extremal graphs with respect to the ABS index. These problems involve characterizing graphs that attain the maximum ABS index within specific graph classes, including: connected graphs with n vertices and p cut-vertices; (ii) connected graphs of order n with vertex k-partiteness; 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.
Keywords
Cite
@article{arxiv.2512.23199,
title = {On extremal graphs with respect to the ABS index},
author = {Swathi Shetty and B. R. Rakshith and Sayinath Udupa N.},
journal= {arXiv preprint arXiv:2512.23199},
year = {2025}
}