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A digraph D is primitive if there is a positive integer k such that there is a walk of length k between arbitrary two vertices of D. The exponent of a primitive digraph is the least such k. Wielandt graph Wn of order n is known as the digraph whose exponent is n2 - 2n + 2, which is the maximum of all the exponents of the primitive digraphs of order n. It is known that the diameter of the multiple direct product of a digraph Wn strictly increases according to the multiplicity of the product. And it stops when it attains to the exponent of Wn . In this paper, we nd the diameter of the direct product of Wielandt graphs.
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참고문헌 (7)
참고문헌 신청
H. Schneider / 2002 / Wielandt's proof of the exponent inequality for primitive non- negative matrices / Linear Algebra Appl 353 : 5 ~ 10
H. Wielandt / 1950 / Unzerleghare, nicht negative Matrizen / Math. Z 52 : 642 ~ 645
J. Moon / 1965 / On the diameter of a graph / Michigan Math. J 12 : 349 ~ 351
M. McAndrew / 1963 / On the product of directed graphs / Proc. Amer. Math. Soc 14 : 101 ~ 108
P. Weischel / 1962 / The Kronecker product of graphs / Proc. Amer. Math. Soc 12 : 47 ~ 52
H. Wielandt / 1950 / Unzerleghare, nicht negative Matrizen / Math. Z 52 : 642 ~ 645
J. Moon / 1965 / On the diameter of a graph / Michigan Math. J 12 : 349 ~ 351
M. McAndrew / 1963 / On the product of directed graphs / Proc. Amer. Math. Soc 14 : 101 ~ 108
P. Weischel / 1962 / The Kronecker product of graphs / Proc. Amer. Math. Soc 12 : 47 ~ 52
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