Geodesic
The improvement of exponent's estimates for primitive graphs
Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 98-100.

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The estimates of exponents of $n$-vertex primitive digraphs are improved. The digraphs considered contain two prime contours whose lengths $l$ and $\lambda$ are coprime numbers. Accessible estimates of the order $O(\max\{l\lambda,f(l,\lambda,n)\})$ are obtained, where $f(l,\lambda,n)$ is a linear polynomial. Primitive digraphs whose exponents are maximal ($n^2-2n+2$, H. Wielandt, 1950), are described completely. The estimates of exponents of $n$-vertex primitive undirected graphs are improved too. In particular, the exponent of an undirected graph is no more $2n-l-1$ where $l$ is the length of the longest cycle with odd length in graph. Primitive undirected graphs whose exponents are maximal ($2n-2$) are described completely. 
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     author = {V. M. Fomichev},
     title = {The improvement of exponent's estimates for primitive graphs},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {98--100},
     publisher = {mathdoc},
     number = {13},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2011_13_a50/}
}
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V. M. Fomichev. The improvement of exponent's estimates for primitive graphs. Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 98-100. http://geodesic.mathdoc.fr/item/PDM_2011_13_a50/

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