The techniques presented in the paper for analyzing the 2-domination number of cylindrical graphs can be extended to various other graph families, particularly those that can be represented as Cartesian products or possess similar structural properties. Some notable examples include:
Grid Graphs: The methods used for cylindrical graphs, particularly the adaptation of wasted domination techniques, can be applied to grid graphs. The authors have previously explored domination-type parameters in grids, making this a natural extension.
Torus Graphs: As a generalization of cylindrical graphs, torus graphs can also be analyzed using similar techniques. The toroidal structure allows for the exploration of 2-domination in a periodic manner, which could yield interesting results.
Product Graphs: Beyond paths and cycles, other product graphs, such as the Cartesian product of two cycles or two paths, could benefit from the matrix operations and tropical algebra techniques discussed in the paper.
Bipartite Graphs: The methods could be adapted to study the 2-domination number in specific classes of bipartite graphs, especially those that can be decomposed into simpler components.
Regular Graphs: The techniques may also be applicable to regular graphs, where uniformity in vertex degree could simplify the analysis of domination parameters.
By leveraging the matrix operations and the concept of wasted domination, researchers can explore the 2-domination number in these and other graph families, potentially uncovering new insights and results.