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http://dx.doi.org/10.4134/BKMS.2011.48.3.637

COMPETITION INDICES OF STRONGLY CONNECTED DIGRAPHS  

Cho, Han-Hyuk (Department of Mathematics Education Seoul National University)
Kim, Hwa-Kyung (Department of Mathematics Education Sangmyung University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.3, 2011 , pp. 637-646 More about this Journal
Abstract
Cho and Kim [4] and Kim [6] introduced the concept of the competition index of a digraph. Cho and Kim [4] and Akelbek and Kirkland [1] also studied the upper bound of competition indices of primitive digraphs. In this paper, we study the upper bound of competition indices of strongly connected digraphs. We also study the relation between competition index and ordinary index for a symmetric strongly connected digraph.
Keywords
competition graph; m-step competition graph; competition index; competition period; scrambling index; symmetric digraph;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 4  (Related Records In Web of Science)
Times Cited By SCOPUS : 4
연도 인용수 순위
1 H. K. Kim, Competition indices of tournaments, Bull. Korean Math. Soc. 45 (2008), no. 2, 385-396.   DOI   ScienceOn
2 B. Liu and H.-J. Lai, Matrices in Combinatorics and Graph Theory, Kluwer Academic Publishers, 2000.
3 J. Shao, The exponent set of symmetric primitive matrices, Scientia Sinica Ser. A 30 (1987), no. 4, 348-358.
4 J. Shao and Q. Li, The indices of convergence reducible Boolean matrices, Acta Math. Sinica 33 (1990), 13-28.
5 J. Shen, Proof of a conjecture about the exponent of primitive matrics, Linear Algebra and Its Appl. 216 (1995), 185-203.   DOI   ScienceOn
6 M. Akelbek and S. Kirkland, Coefficients of ergodicity and the scrambling index, Linear Algebra Appl. 430 (2009), no. 4, 1111-1130.   DOI   ScienceOn
7 R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge University Press, 1991.
8 H. H. Cho, Indices of irreducible Boolean matrix, J. Korean Math. Soc. 30 (1993), no. 2, 267-274.
9 H. H. Cho and H. K. Kim, Competition indices of digraphs, Proceedings of workshop in combinatorics (2004), 99-107.
10 H. H. Cho, S.-R. Kim, and Y. Nam, The m-step competition graph of a digraph, Discrete Appl. Math. 105 (2000), no. 1-3, 115-127.   DOI   ScienceOn