A matrix characterization of interval and proper interval graphs

In this work a matrix representation that characterizes the interval and proper interval graphs is presented, which is useful for the efficient formulation and solution of optimization problems, such as the kk-cluster problem. For the construction of this matrix representation every such graph is associated with a node versus node zero–one matrix. In contrast to representations used in most of the previous work, the proposed matrix characterization does not make use of the maximal cliques in the graph investigated.