張潔敏, 高玉斌

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一類階本原圖的廣義Competition指數(shù)

張潔敏*, 高玉斌

(中北大學(xué) 數(shù)學(xué)系, 山西 太原, 030051)

本原圖; 途徑; 廣義competition指數(shù)

2009年, 文獻(xiàn)[2]中作者提出了本原圖的Scrambling指數(shù)的概念, 并在文獻(xiàn)[3]中刻畫了達(dá)到最大Scrambling指數(shù)的本原圖. 2010年, 文獻(xiàn)[4]中作者將本原指數(shù)與Scrambling指數(shù)推廣到廣義Competition指數(shù), 并對(duì)指數(shù)所達(dá)到的上界進(jìn)行了極圖刻畫.

[1] Brualdi R A, Ryser H J. Combinatorial Matrix Theory [M]. Cambridge: Cambridge University Press, 1991.

[2] Akelbek M, Kirkland S. Coefficients of ergodicity and the scrambling index [J]. Linear Algebra and its Applications, 2009, 430: 1111—1130.

[3] Akelbek M, Kirkland S. Primitive digraphs with the largest scrambling index [J]. Linear Algebra and its Applications, 2009, 430: 1099—1110.

[4] Kim H K. Generalized competition index of a primitive digraph [J]. Linear Algebra and its Applications, 2010, 433: 72—79.

[5] Kim H K, Pank S G. A bound of generalized competition index of a primitive digraph [J]. Linear Algebra and its Applications, 2012, 436: 86—98.

ZHANG JieMin, GAO YuMin

(Department of Mathematics, North University of China, Taiyuan 030051, China)

primitive digraph; walk; generalized competition index

O 157.5

1672-6146(2014)01-0004-03

10.3969/j.issn.1672-6146.2014.01.002

通訊作者email: 1367356120@qq.com.

2014-01-08

國(guó)家自然科學(xué)基金資助項(xiàng)目(11071227); 山西省回國(guó)留學(xué)人員科研資助項(xiàng)目(2012-070).

(責(zé)任編校:劉曉霞)