ABSTRACT
Given disjoint non-empty subsets S and T of , a digraph D with the vertex set is called a directed Toeplitz graph provided the arc occurs if and only if or . We investigate strong connectivity and primitivity of directed Toeplitz graphs. We prove that any primitive directed Toeplitz graph with vertices has exponent at least 3 and for each , there is a primitive directed Toeplitz graph of order n which has exponent 3. By Wielandt's result, we know that for a primitive digraph D of order n. We characterize the primitive directed Toeplitz graph, for which the upper bound it attained.
Disclosure statement
No potential conflict of interest was reported by the author(s).