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http://dx.doi.org/10.4134/BKMS.2008.45.2.385

COMPETITION INDICES OF TOURNAMENTS  

Kim, Hwa-Kyung (Department of Mathematics Education Sangmyung University)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.2, 2008 , pp. 385-396 More about this Journal
Abstract
For a positive integer m and a digraph D, the m-step competition graph $C^m$ (D) of D has he same set of vertices as D and an edge between vertices u and v if and only if there is a vertex x in D such that there are directed walks of length m from u to x and from v to x. Cho and Kim [6] introduced notions of competition index and competition period of D for a strongly connected digraph D. In this paper, we extend these notions to a general digraph D. In addition, we study competition indices of tournaments.
Keywords
competition graph; m-step competition graph; competition index; competition period; tournament;
Citations & Related Records

Times Cited By Web Of Science : 10  (Related Records In Web of Science)
Times Cited By SCOPUS : 9
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1 H. H. Cho, S.-R. Kim, and Y. Nam, The m-step competition graph of a digraph, Discrete Appl. Math. 105 (2000), 115-127   DOI   ScienceOn
2 J. Shen, Proof of a conjecture about the exponent of primitive matrics, Linear Algebra and Its Appl. 216 (1995), 185-203   DOI   ScienceOn
3 B. Zhou and J. Shen, On generalized exponents of tournaments, Taiwanese J. Math. 6 (2002), 565-572   DOI
4 B. R. Heap and M. S. Lynn, The structure of powers of nonnegative matrices, SIAM J. Appl. Math. 14 (1966), 610-640   DOI   ScienceOn
5 B. Liu and H. J. Lai, Matrices in Combinatorics and Graph Theory, Kluwer Academic Publishers, 2000
6 J. Shao and Q. Li, The indices of convergence reducible Boolean matrices, Acta Math. Sinica 33 (1990), 13-28
7 R. A. Brualdi and B. L. Liu, Generalized exponents of primitive directed graphs, J. Graph Theory 14 (1991), 483-499   DOI
8 S.-R. Kim, Competition graphs and scientific laws for food webs and other systems, Ph. D. Thesis, Rutgers University, 1988
9 R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge University Press, 1991
10 H. J. Greenberg, J. R. Lundgren, and J. S. Maybee, Inverting graphs of rectangular matrices, Discrete Appl. Math. 8 (1984), 255-265   DOI   ScienceOn
11 R. A. Brualdi and J. Shao, Generalized exponents of primitive symmetric digraphs, Discrete Appl. Math. 74 (1997), 275-293   DOI   ScienceOn
12 J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, North-Holland, New York, 1976
13 H. H. Cho, Indices of irreducible Boolean matrix, J. Korean Math. Soc. 30 (1993), 78-85
14 H. H. Cho and H. K. Kim, Competition indices of digraphs, Proceedings of workshop in combinatorics (2004), 99-107
15 J. E. Cohen, Food Webs and Niche Space, Princeton Univ. Press, Princeton, NJ, 1978
16 J. W. Moon and N. J. Pullman, On the power of tournament matrices, J. Combinatorial Theory 3 (1967), 1-9   DOI
17 J. Shao, The exponent set of symmetric primitive matrices, Scientia Sinica, Ser. A 30 (1987), 348-358
18 J. Shao and S.-G. Hwang, Generalized exponents of non-primitive graphs, Linear Algebra Appl. 279 (1998), 207-225   DOI   ScienceOn