The degree distribution in unlabelled $2$-connected graph families

Veronika Kraus
2010 Discrete Mathematics & Theoretical Computer Science  
International audience We study the random variable $X_n^k$, counting the number of vertices of degree $k$ in a randomly chosen $2$-connected graph of given families. We prove a central limit theorem for $X_n^k$ with expected value $\mathbb{E}X_n^k \sim \mu_kn$ and variance $\mathbb{V}X_n^k \sim \sigma_k^2n$, both asymptotically linear in $n$, for both rooted and unrooted unlabelled $2$-connected outerplanar or series-parallel graphs.
doi:10.46298/dmtcs.2773 fatcat:ooff7obzlfhsvh2hgq2oxk6mdu