Let G be a simple, finite, undirected graph with n vertices. The main purpose of this paper introduces the concepts of the minimum covering Gutman Estrada index, the minimum covering Seidel Estrada index, the minimum covering distance Estrada index, the minimum covering Randi´c Estrada index, the minimum covering Harary Estrada index, and the minimum covering color Estrada index of a graph. First, we compute the new concepts for some of the graphs, such as cocktail party, star, crown, complete and complete bipartite. Moreover, we establish upper and lower bounds for the new concepts.
