The estimates of exponents for primitive graphs

The estimates of exponents of $n$-vertex primitive digraphs and undirected graphs are improved. The digraphs considered contain two prime contours with coprime lengths $l$ and $\lambda$. For them, accessible estimates of the order $\mathrm O(\max\{l\lambda,f(l,\lambda,n)\}$ are obtained, where $f(l,\lambda,n)$ is a linear polynomial. The exponent of undirected graph is no more $2n-l-1$, where $l$ is the length of the longest cycle with odd length in graph. Primitive digraphs with maximal exponent ($n^2-2n+2$, H. Wielandt, 1950) and undirected graphs with maximal exponent ($2n-2$) are completely described.