Generalized exponents of primitive two-colored digraphs

Abstract

A l-colored digraph D ( l) is primitive if there exists a nonnegative integer vector α such that for each ordered pair of vertices x and y (not necessarily distinct), there exists an α-walk in D ( l) from x to y. The exponent of the primitive l-colored digraph D ( l) is defined to be the minimum value of the sum of all coordinates of α taken over all such α. In this paper, we generalize the concept of exponent of a primitive l-colored digraph by introducing three types of generalized exponents. Further, we study the generalized exponents of primitive two-colored Wielandt digraphs.