Irreversible k-Threshold Number Ck(G) and Saturation Probability P[G] for Corona Product and Double Corona Product Graphs

We discuss the Irreversible k-conversion process for graphs, where a vertex becomes saturated and remains saturated indefinitely if at least k of its neighbors are saturated. We investigate sets S0, which when initially saturated, lead to complete graph saturation. We are interested in the minimum |S0| = Ck(G), called the k-threshold number. We consider the construction of the Corona Product Graphs (of Cn and Kp). Additionally, we extend our analysis by defining and exploring Double Corona Product Graphs (of Cn and Kp). Then we incorporate probabilistic methods to assess how saturation is affected by randomly selecting S0, when |S0| = Ck(G). Our findings provide insights into the relationship between graph structure, probabilistic behavior, and saturation dynamics, with applications in epidemiology and social influence modeling.