Exponents of two-colored digraphs with two cycles

Gao, Yubin; Shao, Yanling

doi:10.1016/j.laa.2005.05.004

Cited by 18 publications

(48 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The concept of the exponent of a nonnegative matrix pair arises naturally in the study of finite Markov chains, and some results have already been obtained ( [1], [2], [3], [4], [5]). We consider the two-colored digraphs that have at least one red arc and one blue arc, and whose uncolored digraph is the digraph as given in Fig.…”

Section: R(w) B(w)mentioning

confidence: 99%

“…1. In [4], we considered D with m = s + 2 and gave the set of exponents of families of D. In [5], we considered D with m = s + 3 and gave the bounds on the exponents and characterizations of extremal two-colored digraphs. In this paper we consider D with m = s + 4 (that is t = 3), n 9, give bounds on the exponents and characterizations of extremal twocolored digraphs.…”

Section: P R O O F Note Thatmentioning

confidence: 99%

See 1 more Smart Citation

Exponents of two-colored digraphs

Shao

Gao

2009

Czech Math J

Self Cite

View full text Add to dashboard Cite

Section: R(w) B(w)mentioning

confidence: 99%

Section: P R O O F Note Thatmentioning

confidence: 99%

Exponents of two-colored digraphs

Shao

Gao

2009

Czech Math J

Self Cite

View full text Add to dashboard Cite

“…In fact, there is a one-to-one relationship between nonnegative matrix pairs and two-colored digraphs.By studying the exponent of associated directed digraph of nonnegative matrix pairs, that is two-colored directed digraphs, the problem of nonnegative matrix, the upper bound and the lower bound of primitive exponent, the characterizations of extremeal digraphs etc can be solved.Some results have already been obtained [4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

The Primitivity and Primitive Exponents of a Class of Nonnegative Matrix Pairs

Mei-jin¹

2017

Proceedings of the 7th International Conference on Education, Management, Information and Mechanical Engineering (EMIM 2017)

View full text Add to dashboard Cite

Abstract. It is a brand-new research in combinatorial matrix theory to extend the exponent of traditional single nonnegative primitive matrix to the exponent of nonnegative primitive matrix pairs. With the knowledge of graph theory, the problem of primitive exponent of nonnegative matrix pairs can be transformed into the associated directed digraph of nonnegative matrix pairs, that is two-colored digraphs. A class of two-colored digraphs whose uncolored digraph has 4 2 n+ vertices and consists of one (4 1) n + -cycle and one n-cycle is considered. The primitive conditions, the upper bound, the lower bound, and the characterizations of extremal two-colored digraphs are given. The results provide a basis for the study of the exponent of nonnegative primitive matrix pairs and the exponent of nonnegative primitive matrix tuples in the general case.

show abstract

“…The concept of the exponent of a nonnegative matrix pair arises in the study of finite Markov chains [4], and some results have already been obtained [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%