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 Kk+1-free, while the key property in the second result is that G contains a Kk. 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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