ABSTRACT
We characterize the linear operators on simple undirected graphs on n vertices that strongly preserve sets defined by the cochromatic number and those that strongly preserve sets defined by the clique partition number. The clique partition number of G is the minimum number of cliques whose edge disjoint union is G while the cochromatic number of G is the minimum number of complete graphs whose vertex disjoint union is a subgraph of G with the same number of vertices as G.
