Domination and Total Domination in Johnson graphs

Abstract

In this paper we study domination and total domination of Johnson graphs $J(n,k)$. We establish monotonicity results proving that both $γ(J(n,k))$ and $γ_t(J(n,k))$ are non-decreasing with respect to $n$. We compute exact values for $γ_t(J(n,k))$ in specific cases, showing that $γ_t(J(n,2))=\lceil\frac{2}{3}(n-1)\rceil$ for $n\geq 4$, and determining $γ_t(J(n,3))$ for $n\geq 6$, which depends quadratically on $n$.