EXPONENTS OF CARTESIAN PRODUCTS OF TWO DIGRAPHS OF SPECIAL ORDERS

Title & Authors
EXPONENTS OF CARTESIAN PRODUCTS OF TWO DIGRAPHS OF SPECIAL ORDERS
Kim, Byeong-Moon; Rho, Yoo-Mi;

Abstract
In this paper, we find the maximum exponent of D $\small{{\times}}$ E, the cartesian product of two digraphs D and E on n, n + 2 vertices, respectively for an even integer $\small{n\geq4}$. We also characterize the extrema cases.
Keywords
exponents;digraphs;Cartesian products;Wielandt graphs;Frobenius numbers;
Language
English
Cited by
References
1.
A. Brauer, On a problem of partitions, Amer. J. Math. 64 (1942), 299-312.

2.
B. M. Kim, B. C. Song, and W. Hwang, Wielandt type theorem for Cartesian product of digraphs, Linear Algebra Appl. 429 (2008), no. 4, 841-848.

3.
R. Lamprey and B. Barnes, Primitivity of products of digraphs, Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1979), pp. 637-644, Congress. Numer., XXIII-XXIV, Utilitas Math., Winnipeg, Man., 1979.

4.
B. L. Liu, B. D. McKay, N. C. Wormald, and K. Zhang, The exponent set of symmetric primitive (0; 1) matrices with zero trace, Linear Algebra Appl. 133 (1990), 121-131.

5.
J. B. Roberts, Note on linear forms, Proc. Amer. Math. Soc. 7 (1956), 465-469.

6.
J. Y. Shao, The exponent set of symmetric primitive matrices, Sci. Sinica Ser. A 9 (1986), 931-939.

7.
H. Wielandt, Unzerlegbare, nicht negative Matrizen, Math. Z. 52 (1950), 642-648.