The minimum exponent of the primitive digraphs on the given number of arcs

• Autorzy: Rosiak J.
• Języki publikacji: EN

Abstrakty

EN

Primitive digraphs on n vertices, k arcs and girth s are considered. By a(n, k, s) we mean the minimum exponent taken over all such digraphs. We estimate the number a(n, k, s) using the Frobenius number for special values of k and s.

Słowa kluczowe

EN

primitive directed graph; exponent; Frobenius number

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2004
• Tom: Vol. 24, no. 2
• Strony: 197--202
• Opis fizyczny: Bibliogr. 4 poz., rys.

Twórcy

autor

Rosiak J.

• Technical University of Szczecin, Institute of Mathematics, ul. Aleja Piastów 48/49, 70-310 Szczecin, Poland,

Bibliografia

• [1] Brualdi R. A., Ryser H. J.: Combinatorial Matrix Theory. Cambridge University Press, 1991.
• [2] Dulmage A., Mendelsohn N.: Gaps in the exponent set of primitive matrices. Ilinois J.Math. 8 (1964), 642-656.
• [3] Kemeny J.G., Snell J.L.: Finite Marcov Chains. Van Nostrand, Princeton, 1960.
• [4] Zhengke M., Kemin Z.: The minimum norm of solutions of a Boolean matrix equation Ak= I. Graph Theory of New York XXXVIII (2000), 7-11.