COMPETITION INDICES OF TOURNAMENTS

Kim, Hwa-Kyung

doi:10.4134/BKMS.2008.45.2.385

Title & Authors

COMPETITION INDICES OF TOURNAMENTS
Kim, Hwa-Kyung;

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;

Language

English

Cited by

2time(s) in KSCD

1.

COMPETITION INDICES OF STRONGLY CONNECTED DIGRAPHS,;;

대한수학회보, 2011. vol.48. 3, pp.637-646

2.

THE COMPETITION INDEX OF A NEARLY REDUCIBLE BOOLEAN MATRIX,;;

대한수학회보, 2013. vol.50. 6, pp.2001-2011

16time(s) in CrossRef

1.

COMPETITION INDICES OF STRONGLY CONNECTED DIGRAPHS, Bulletin of the Korean Mathematical Society, 2011, 48, 3, 637

2.

Generalized competition indices of symmetric primitive digraphs, Discrete Applied Mathematics, 2012, 160, 10-11, 1583

3.

Generalized competition index of primitive digraphs, Acta Mathematicae Applicatae Sinica, English Series, 2017, 33, 2, 475

4.

A matrix sequence{Γ(Am)}m=1∞might converge even if the matrix A is not primitive, Linear Algebra and its Applications, 2013, 438, 5, 2306

5.

THE COMPETITION INDEX OF A NEARLY REDUCIBLE BOOLEAN MATRIX, Bulletin of the Korean Mathematical Society, 2013, 50, 6, 2001

6.

On generalized competition index of a primitive tournament, Discrete Mathematics, 2011, 311, 23-24, 2657

7.

Generalized scrambling indices of a primitive digraph, Linear Algebra and its Applications, 2010, 433, 11-12, 1798

8.

A bound of generalized competition index of a primitive digraph, Linear Algebra and its Applications, 2012, 436, 1, 86

9.

Generalized competition index of a primitive digraph, Linear Algebra and its Applications, 2010, 433, 1, 72

10.

Bounds on the generalized μ-scrambling indices of primitive digraphs, International Journal of Computer Mathematics, 2012, 89, 1, 17

11.

On the matrix sequence for a Boolean matrix A whose digraph is linearly connected, Linear Algebra and its Applications, 2014, 450, 56

12.

Characterization of irreducible Boolean matrices with the largest generalized competition index, Linear Algebra and its Applications, 2015, 466, 218

13.

The scrambling index of primitive digraphs, Computers & Mathematics with Applications, 2010, 60, 3, 706

14.

Generalized competition index of an irreducible Boolean matrix, Linear Algebra and its Applications, 2013, 438, 6, 2747

15.

A bound on the generalized competition index of a primitive matrix using Boolean rank, Linear Algebra and its Applications, 2011, 435, 9, 2166

16.

Scrambling index set of primitive digraphs, Linear Algebra and its Applications, 2013, 439, 7, 1886

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