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arXiv · 2503.01343

Extremal graphs with maximum complementary second Zagreb index

Hui Gao
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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 $n$ with the maximum complementary second Zagreb index. In this paper, we confirm their conjecture.

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Hui Gao. 2025-03-03. Extremal graphs with maximum complementary second Zagreb index. https://arxiv.org/abs/2503.01343

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