A necessary and sufficient condition is established for doubly-connectedness in $b$-row and $k$-column designs in which all cells are filled. A necessary condition for doubly-connectedness in a generalized two-way elimination of heterogeneity designs is provided and a property of doubly-connected designs is given.
"On Connectedness in Two-Way Elimination of Heterogeneity Designs." Ann. Statist. 3 (3) 730 - 735, May, 1975. https://doi.org/10.1214/aos/1176343137