  The smallest set Q of vertices of a graph G, such that every path on 3
vertices, has at least one vertex in Q, is a minimum 3-covering of G. By
attaching loops of weight 1 to the vertices of G we can find the eigenvalues
associated with G, and hence the minimum 3-covering energy of G. In this paper
we characterize graphs with 3-coverings in terms of non-Q-covered edges, and we
determine the minimum 3-covering energy of a star graph with m rays each of
length 2.
