Rings Domination Number of Some Mycielski Graphs

A set S of a graph G = (V (G);E(G)) is a rings dominating set if S is a dominating set and for every vertex in the complement of S has atleast two adjacent vertices. The caridinality of the minimum rings dominating set is the rings domination number of graph G, denoted by \(\gamma\)ri(G). In this paper we determine the exact rings domination number of the mycielski graphs of path graph, cycle graph, and crown graph including its parameter.