Generalized Indices Of Boolean Matrices

There is an extensive literature on the index theory of Boolean matrices. We studied three types of generalized indices of Boolean matrices. We fa-cus on the third type of generalized (primitive) exponents of and the first type of generalized indices of convergence for general Boolean matrices. We determine the maximum values of the third type of generalized (primitive) exponents for all n x n Boolean matrices, characterize the extreme matrices, i.e., those Boolean matrices whose third type of generalized exponents achieve the maximum values. We also obtain similar results on nearly reducible Boolean matrices. We determine the maximum values of the first type of indices of convergence of n x n Boolean matrices, reducible matrices, critically reducible matrices respectively, characterize the corresponding extreme matrices. Finally we disscuss the weak exponents of irreducible matrices.