2024/02/20 by Gerbner, Dániel
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2402.13403
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+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.