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English version: Journal of Applied and Industrial Mathematics, 2017, 11:1, 2639 

Volume 24, No 1, 2017, P. 97119 UDC 519.17
Keywords: primitive matrix, primitive graph, exponent, local primitivity of a matrix (graph), local exponent. DOI: 10.17377/daio.2017.24.519 Vladimir M. Fomichev ^{1,2} Received 7 December 2015 References[1] K. G. Kogos and V. M. Fomichev, Positive properties of nonnegative matrices, Prikl. Diskretn. Mat., No. 4, 5–13, 2012 [Russian].[2] S. N. Kyazhin and V. M. Fomichev, On primitive sets of natural numbers, Prikl. Diskretn. Mat., No. 2, 5–14, 2012 [Russian]. [3] S. N. Kyazhin and V. M. Fomichev, Local primitiveness of graphs and nonnegative matrices, Prikl. Diskretn. Mat., No. 3, 68–80, 2014 [Russian]. [4] L. Ya. Okunev, Kratkii kurs teorii chisel (A Brief Course in Number Theory), Uchpedgiz, Moscow, 1956 [Russian]. [5] V. N. Sachkov and V. E. Tarakanov, Kombinatorika neotritsatel’nykh matrits, TVP, Moscow, 2000 [Russian]. Translated under the title Combinatorics of nonnegative matrices, AMS, Providence, 2002 (Transl. Math. Monogr., Vol. 213). [6] R. A. Brualdi and B. Liu, Generalized exponents of primitive directed graphs, J. Graph Theory, 14, 483–499, 1990. [7] Y. Huang and B. Liu, Generalized $r$exponents of primitive digraphs, Taiwan. J. Math., 15, No. 5, 1999–2012, 2011. [8] B. Liu, Generalized exponents of Boolean matrices, Linear Algebra Appl., 373, 169–182, 2003. [9] Z. Miao and K. Zhang, The local exponent sets of primitive digraphs, Linear Algebra Appl., 307, 15–33, 2000. [10] J. L. Ramírez Alfonsín, The Diophantine Frobenius Problem, Oxf. Univ. Press, Oxford, 2005 (Oxf. Lect. Ser. Math. Appl., Vol. 30). [11] J. Shao, J. Wang, and G. Li, Generalized primitive exponents with complete characterizations of the extreme digraphs, Chin. Ann. Math., Ser. A, 15, No. 5, 518–523, 1994 [Chinese]. Translated in Chin. J. Contemp. Math., 15, No. 4, 317–324, 1994. [12] J. Shen and S. Neufeld, Local exponents of primitive digraphs, Linear Algebra Appl., 268, 117–129, 1998. 

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