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 $\gamma (J(n,k))$ and ${\gamma }_t(J(n,k))$ are non-decreasing with respect to $n$. We compute exact values for ${\gamma }_t(J(n,k))$ in specific cases, showing that ${\gamma }_t(J(n,2))=\lceil \frac{2}{3}(n-1)\rceil$ for $n\ge 4$, and determining ${\gamma }_t(J(n,3))$ for $n\ge 6$, which depends quadratically on $n$.

arXiv comment28 pages, 9 figures, 3 tables