Extremal graphs with maximum complementary second Zagreb index
Combinatorics
2025-03-04 v1
Abstract
Recently, a couple of degree-based topological indices, defined using a geometrical point of view of a graph edge, have attracted significant attention and being extensively investigated. Furtula and Oz [Complementary Topological Indices, \textit{MATCH Commun. Math. Comput. Chem.\/} \textbf{93} (2025) 247--263] introduced a novel approach for devising ``geometrical'' topological indices and focused special attention on the complementary second Zagreb index as a representation of the introduced approach. In the same paper, they also conjectured the maximal graphs of order with the maximum complementary second Zagreb index. In this paper, we confirm their conjecture.
Keywords
Cite
@article{arxiv.2503.01343,
title = {Extremal graphs with maximum complementary second Zagreb index},
author = {Hui Gao},
journal= {arXiv preprint arXiv:2503.01343},
year = {2025}
}