On fully indecomposable exponent for primitive boolean matrices with symmetric ones

Abstract

If A is a primitive matrix, then there is a smallest power of A (its fully indecomposable exponent) which is fully indecomposable, and a smallest power of A (its strict fully indecomposable exponent) starting from which all powers are fully indecomposable. We obtain bounds on these two exponents for primitive Boolean matrices with symmetric one's.