Core and coritivity of a system (IV) - relations between a system and its complement

The coritivity, h(G), of a connected graph G, is defined by h(G)=max{ω(G-S)-|S|}, where ω(G) denotes the number of components of a graph G, C(G) denotes the collection of cut-sets of G. In this paper, the norion of complementary coritivity is proposed, and the relations between coritivity and its complement are studied, for example, two bounds, Nordaus-Gaddum problems and some foundational properties etc.