References
- R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge University Press, 1991
- R. A. Brualdi and B. L. Liu, Generalized exponents of primitive directed graphs, J. Graph Theory 14 (1991), 483-499 https://doi.org/10.1002/jgt.3190140413
- R. A. Brualdi and J. Shao, Generalized exponents of primitive symmetric digraphs, Discrete Appl. Math. 74 (1997), 275-293 https://doi.org/10.1016/S0166-218X(96)00077-7
- J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, North-Holland, New York, 1976
- H. H. Cho, Indices of irreducible Boolean matrix, J. Korean Math. Soc. 30 (1993), 78-85
- H. H. Cho and H. K. Kim, Competition indices of digraphs, Proceedings of workshop in combinatorics (2004), 99-107
- H. H. Cho, S.-R. Kim, and Y. Nam, The m-step competition graph of a digraph, Discrete Appl. Math. 105 (2000), 115-127 https://doi.org/10.1016/S0166-218X(00)00214-6
- J. E. Cohen, Food Webs and Niche Space, Princeton Univ. Press, Princeton, NJ, 1978
- H. J. Greenberg, J. R. Lundgren, and J. S. Maybee, Inverting graphs of rectangular matrices, Discrete Appl. Math. 8 (1984), 255-265 https://doi.org/10.1016/0166-218X(84)90123-9
- B. R. Heap and M. S. Lynn, The structure of powers of nonnegative matrices, SIAM J. Appl. Math. 14 (1966), 610-640 https://doi.org/10.1137/0114052
- S.-R. Kim, Competition graphs and scientific laws for food webs and other systems, Ph. D. Thesis, Rutgers University, 1988
- B. Liu and H. J. Lai, Matrices in Combinatorics and Graph Theory, Kluwer Academic Publishers, 2000
- J. W. Moon and N. J. Pullman, On the power of tournament matrices, J. Combinatorial Theory 3 (1967), 1-9 https://doi.org/10.1016/S0021-9800(67)80009-7
- J. Shao, The exponent set of symmetric primitive matrices, Scientia Sinica, Ser. A 30 (1987), 348-358
- J. Shao and S.-G. Hwang, Generalized exponents of non-primitive graphs, Linear Algebra Appl. 279 (1998), 207-225 https://doi.org/10.1016/S0024-3795(98)10014-9
- J. Shao and Q. Li, The indices of convergence reducible Boolean matrices, Acta Math. Sinica 33 (1990), 13-28
- J. Shen, Proof of a conjecture about the exponent of primitive matrics, Linear Algebra and Its Appl. 216 (1995), 185-203 https://doi.org/10.1016/0024-3795(93)00132-J
- B. Zhou and J. Shen, On generalized exponents of tournaments, Taiwanese J. Math. 6 (2002), 565-572 https://doi.org/10.11650/twjm/1500407480
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