Forcing Clique Domination in Graphs

The clique domination number of some special graphs such as paths, cycles, complete graphs, generalized wheels, generalized fans, and complete bipartite graphs is presented. The forcing clique domination number of these graphs, along with binary operations such as join, corona, and lexicographic product of two graphs, is also determined. Connected graphs with forcing clique domination number equal to $0$, $1$, or $a$, where $a$ is greater than $1$ but less than the clique domination number, are characterized. Necessary and sufficient conditions for the forcing clique domination number to be equal to the clique domination number are given. Since some of the graphs in this study do not have a clique dominating set, the forcing clique domination number is undefined in those cases.