A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γ<inf>c</inf>(G)=2, 3 and characterize such graphs. Also, we characterize the k-γ-vertex (edge) critical graphs and k-γ<inf>c</inf>-vertex (edge) critical graphs for k=2, 3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Chithra, M. R., & Vijayakumar, A. (2015). Domination criticality in product graphs. AKCE International Journal of Graphs and Combinatorics, 12(1), 19–25. https://doi.org/10.1016/j.akcej.2015.06.003