On Rings Domination of Total Graph of Some Graph Families

For a nontrivial connected graph G with no isolated vertex, nonempty subset D \(\subseteq\) V (G) is rings dominating set if and for each vertex \(\upsilon\) \(\in\) \ adjacent to at least two vertices in D. Thus, the of all D, \(\mid\)N(\(\upsilon\)) \(\cap\) (V D)\(\mid\) \(\ge\) 2. Moreover, called minimum smallest size given graph. The cardinality domination number G, denoted by \(\gamma\)ri(G). Here, we determine how constructed total some families inclusion generated conditions this type provide their respective number.