Minimum Clique-clique Dominating Laplacian 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 Í C(G) is said to be a cc-dominating set (CCD-set) if every clique in G is ccdominated by some clique in L. The cc-domination number γcc = γcc(G) is the order of a minimum cc-dominating set of G. In this paper we introduce minimum cc-dominating Laplacian energy of the graph denoting it as LEcc(G). It depends both on underlying graph of G and its particular minimum cc-dominating set (γcc-set) of G. Upper and lower bounds for LEcc(G) are established.