Minimum clique-clique dominating energy of a graph

Let C(G) denotes the set of all cliques of a graph G. Two cliques in G are adjacent if there is a vertex incident on them. Two cliques c₁, c₂ ∈ C(G) are said to clique-clique dominate (cc-dominate) each other if there is a vertex incident with c₁ and c₂ . A set L ⊆ C(G) is said to be a cc-dominating set (CCD-set) if every clique in G is cc-dominated by some clique in L. The cc-domination number γ_cc = γ_cc(G) is the order of a minimum cc-dominating set of G. In this paper we introduce minimum cc-dominating energy of the graph denoting it as E_cc (G). It depends both on underlying graph of G and its particular minimum cc-dominating set (γ_cc-set) of G. Upper and lower bounds for E_cc (G) are established.