Applications of realizable Boolean matrices in graph theory

This paper gives some applications of realizable Boolean matrices in graph theory. We apply realizable Boolean matrices to characterize clique, maximal clique, maximum clique and clique cover in graph theory. Particularly, we prove that the content of a realizable Boolean matrix is exactly the clique cover number of its corresponding undirected graph, and present algorithms to determine the content and a realizing matrix with minimum number of columns of a given realizable Boolean matrix and a minimum clique cover of an undirected graph, respectively.