(untitled) (European Journal of Pure and Applied Mathematics, 2025)
A certified dominating set S is a dominating set of a graph G, if every vertex in S has either zero or at least two neighbours in V §. The minimum cardinality of certified dominating set of G is the certified domination number of G denoted by γcer(G). We defined certified domination subdivision number Sd+γcer (G) [Sd−γcer (G)] of a graph G to be the minimum number of edges that must be subdivided (where no edge in G can be subdivided more than once) in order to construct a graph with a certified domination number larger [lesser] than the certified domination number of G. In this paper, we determine the values of certified domination subdivision number for certain classes of graphs including circulant graphs [Cn(1, 2) and Cn(1, 3)] and petersen graphs [P(n, 1) and P(n, 2)].