Let IGI be the number of vertices of a graph G and to(G) be the density of G. We call a graph G packed if the clique graph K(G) of G has exactly 2 IGI-O'(G) cliques. We correct the characterization of clique graphs of packed graphs given in Theorem 3.2 of Hedman [3]. All graphs considered here are finite, undirected and simple. We denote the number of vertices of a graph G by I al. A clique of a graph G is a maximal complete subgraph of G. The clique graph K(G) of a graph G is the intersection graph of the vertex sets of cliques of G. The density co(G) of a graph G is the number of the vertices in the largest clique of G. The graph G is said to be clique-critical if for each vertex v of G, K(G -v) is non-isomorphic to K(G). We call a graph G packed if IK(G)I = 2 Icl-''(c). This definition is well-defined since for every graph G, [K(G)I <~ 2 Icl-Β°'(c) by [3], Theorem 2.1.
We write H < G if the graph H is an induced subgraph of the graph G. An 2n-Neumann graph H2, is the complement of a matching between 2n vertices (see ). Let G1, 62 be two graphs with V(G1) CI V(G2) = ~. The join of G1 and 62, denoted by G1 + G2, is the graph with vertex set V(G1)U V(G2) and edge set
and v β’ V(G2)}. Other definitions not here will be found in [1]. B. Hedman [3] proved the following Theorem. Theorem A. For a graph G, let IGI-co(G) = n. If IK(G)I = 2-, then G > Hz.. We correct the characterization of clique graphs of packed graphs given in [3, Theorem 3.2] as follows: Theorem 1. For a graph G, let IGIco(G)=.. If IK(G)I = 2-, then K(G) is isomorphic to the 2"-Neumann graph HE. or the complete graph K2-.