The Estimates of Exponents for Primitive Graphs | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2011. № 2(12).

The estimates of exponents of n-vertex primitive digraphs and undirectedgraphs are improved. The digraphs considered contain two prime contours with coprimelengths l and A. For them, accessible estimates of the order O(max{lA, f (l,A,n)} are obtained,where f (l, A, n) is a linear polynomial. The exponent of undirected graph is no more2n - l - 1, where l is the length of the longest cycle with odd length in graph. Primitivedigraphs with maximal exponent (n2 - 2n + 2, H. Wielandt, 1950) and undirected graphswith maximal exponent (2n - 2) are completely described.