Geodesic
Estimates for exponent of some graphs by Frobenius's numbers of three arguments
Prikladnaâ diskretnaâ matematika, no. 2 (2014), pp. 88-96.

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A formula for Frobenius's numbers of three arguments is given. Estimates for exponent of some superconnected digraphs are obtained using this formula. It is shown that the given estimation is the best in many cases.
Keywords: Frobenius's number, additive semigroup generated by set of numbers, exponent of graph. 
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V. M. Fomichev. Estimates for exponent of some graphs by Frobenius's numbers of three arguments. Prikladnaâ diskretnaâ matematika, no. 2 (2014), pp. 88-96. http://geodesic.mathdoc.fr/item/PDM_2014_2_a6/

[1] Alfonsin J. R., The Diophantine Frobenius Problem, Oxford University Press, 2005 | MR | Zbl

[2] Sylvester J. J., “Problem 7382”, Mathematical Questions from the Educational Times, 37 (1884), 26

[3] Curtis F., “On formulas for the Frobenius number of a numerical semigroup”, Math. Scand., 67 (1990), 190–192 | MR | Zbl

[4] Heap B. R., Lynn M. S., “On a linear Diophantine problem of Frobenius: an improved algorithm”, Numer. Math., 7 (1965), 226–231 | DOI | MR | Zbl

[5] Bocker S., Liptak Z., The “money changing problem” revisited: computing the Frobenius number in time O$(ka_1)$, Technical Report No. 2004-2, Univ. of Bielefeld, Technical Faculty, 2004 | MR

[6] Fomichev V. M., “Ekvivalentnye po Frobeniusu primitivnye mnozhestva chisel”, Prikladnaya diskretnaya matematika, 2014, no. 1(23), 20–26

[7] Brauer A., “On a problem of partitions”, Am. J. Math., 64 (1942), 299–312 | DOI | MR | Zbl

[8] Sachkov V. N., Tarakanov V. E., Kombinatorika neotritsatelnykh matrits, TVP, M., 2000, 448 pp. | MR | Zbl

[9] Kogos K. G., Fomichev V. M., “Polozhitelnye svoistva neotritsatelnykh matrits”, Prikladnaya diskretnaya matematika, 2012, no. 4(18), 5–13

[10] Fomichev V. M., “Otsenki eksponentov primitivnykh grafov”, Prikladnaya diskretnaya matematika, 2011, no. 2(12), 101–112

[11] Berzh K., Teoriya grafov i eë primenenie, IL, M., 1962, 320 pp.

[12] Wielandt H., “Unzerlegbare nicht negative Matrizen”, Math. Zeitschr., 52 (1950), 642–648 | DOI | MR | Zbl