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arXiv · 2402.13403

On extremal values of some degree-based topological indices with a forbidden or a prescribed subgraph

Dániel Gerbner
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Abstract

Xu in 2011 determined the largest value of the second Zagreb index in an $n$-vertex graph $G$ with clique number $k$, and also the smallest value with the additional assumption that $G$ is connected. We extend these results to other degree-based topological indices. The key property of the clique number in the first result is that $G$ is $K_{k+1}$-free, while the key property in the second result is that $G$ contains a $K_{k+1}$. We also extend our investigations to other forbidden/prescribed subgraphs. Our main tool is showing that several degree-based topological indices are equal to the weighted sum of the number of some subgraphs of $G$.

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Dániel Gerbner. 2024-02-20. On extremal values of some degree-based topological indices with a forbidden or a prescribed subgraph. https://arxiv.org/abs/2402.13403

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