一类双色有向图的指数的上界
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摘要
主要利用非负矩阵论与图论的知识研究了一类特殊的双色有向图,其未着色图中只包含两个圈,分别为n-圈和(mn-1)-圈,且这两个圈仅包含两条公共弧。给出了该双圈双色有向图的本原条件,得到了其本原指数的上界,刻画了达到本原指数上界的极图。此研究将非负矩阵论、图论、线性代数等学科有机地结合,进一步推动学科间的交叉和渗透研究。
A special kind of two-colored digraphs is studied using the knowledge of nonnegative matrix theory and graph theory.Its uncolored digraph contains one n-cycle and one(mn-1)-cycle with two common arcs.Some primitive conditions,upper bound on the exponents,and the characterizations of the extremal two-colored digraphs are given.This study combines nonnegative matrix theory,graph theory and linear algebra organically.It promotes the intersection and penetration between disciplines further.
A special kind of two-colored digraphs is studied using the knowledge of nonnegative matrix theory and graph theory.Its uncolored digraph contains one n-cycle and one(mn-1)-cycle with two common arcs.Some primitive conditions,upper bound on the exponents,and the characterizations of the extremal two-colored digraphs are given.This study combines nonnegative matrix theory,graph theory and linear algebra organically.It promotes the intersection and penetration between disciplines further.
引文
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[4]Gao Y B,Shao Y L.On the exponents of two-colored digraphs with two cycles[J].Linear Algebra and Its Applications,2007,57(2):263-276.
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[6]Shao Y L,Gao Y B,Sun L.On the exponents of two-colored digraphs with two cycles[J].Linear and Multilinear Algebra,2009,57(2):185-199.
[7]Huang F Y,Liu B L.Exponents of a class of two-colored digraphs with two cycles[J].Linear Algebra and Its Applications,2008,429(2):658-672.
[8]李茜.一类特殊双色有向图的本原指数[J].江苏师范大学学报:自然科学版,2012,30(4):6-8.
[9]罗美金.一类双色有向图的本原指数上界[J].数学的实践与认识,2013,43(23):142-150.
[10]李茜,罗美金.特殊双色有向图的本原指数[J].曲阜师范大学学报:自然科学版,2015,41(4):48-50.
[11]李茜,罗美金.双色有向图的本原指数的上界[J].北华大学学报:自然科学版,2015,16(5):584-587.
[12]李茜,罗美金.特殊双色有向图的本原指数的上界[J].贵州师范大学学报:自然科学版,2017,35(2):58-60.
[13]罗美金,李茜.一类含有奇数个顶点的三色有向图本原指数上界[J].数学的实践与认识,2017,47(4):209-216.
[14]曲敏,许成,蒋文超.图对数线性模型性质的研究[J].青岛大学学报:自然科学版,2017,30(1):58-60.
[2]Gao Y B,Shao Y L.Exponent of two-colored double directed cycles[J].Journal of Natural Science of Heilongjiang University,2004,21(4):55-58.
[3]Shao Y L,Gao Y B,Sun L.Exponents of a class of two-colored digraphs[J].Linear and Multilinear Algrbra,2005,53(3):175-188.
[4]Gao Y B,Shao Y L.On the exponents of two-colored digraphs with two cycles[J].Linear Algebra and Its Applications,2007,57(2):263-276.
[5]Gao Y B,Shao Y L.Generalized exponents of primitive two-colored digraphs[J].Linear Algebra and Its Applications,2008,430(5):1550-1565.
[6]Shao Y L,Gao Y B,Sun L.On the exponents of two-colored digraphs with two cycles[J].Linear and Multilinear Algebra,2009,57(2):185-199.
[7]Huang F Y,Liu B L.Exponents of a class of two-colored digraphs with two cycles[J].Linear Algebra and Its Applications,2008,429(2):658-672.
[8]李茜.一类特殊双色有向图的本原指数[J].江苏师范大学学报:自然科学版,2012,30(4):6-8.
[9]罗美金.一类双色有向图的本原指数上界[J].数学的实践与认识,2013,43(23):142-150.
[10]李茜,罗美金.特殊双色有向图的本原指数[J].曲阜师范大学学报:自然科学版,2015,41(4):48-50.
[11]李茜,罗美金.双色有向图的本原指数的上界[J].北华大学学报:自然科学版,2015,16(5):584-587.
[12]李茜,罗美金.特殊双色有向图的本原指数的上界[J].贵州师范大学学报:自然科学版,2017,35(2):58-60.
[13]罗美金,李茜.一类含有奇数个顶点的三色有向图本原指数上界[J].数学的实践与认识,2017,47(4):209-216.
[14]曲敏,许成,蒋文超.图对数线性模型性质的研究[J].青岛大学学报:自然科学版,2017,30(1):58-60.