Domination in Johnson graphs J(n, 3) for odd n

Abstract

In 2025 Cornet, Dravec, and Torres determined the domination number ${\hat{I}}^3(J(n,3))$ of the Johnson graph for every even $n\ge 6$, expressing it as a closed form $\ddot{I}{•}_n$ in terms of Fort\textendash{}Hedlund covering numbers, and conjectured the same value for odd $n$. We prove this conjecture: ${\hat{I}}^3(J(n,3))=\ddot{I}{•}_n$ for every odd $n\ge 7$, completing the determination of ${\hat{I}}^3(J(n,3))$ for all $n\ge 6$.

16 pages