本原有向图D{n-t-1,n-t}的广义μ-scrambling指数
|
摘要
用D{n-t-1,n-t}表示具有两个n-t-1长圈、一个n-t长圈的本原有向图.运用数学归纳方法,结合图论及其构造,来研究此类本原图,得到该本原有向图的λ重下μ-scrambling指数及λ重上μ-scrambling指数.
Denote the primitive digraph with two n-t-1-cycles and one n-t-cycle by D{n-t-1,n-t}.By using the graph theory and Combining the Mathematical construction method with inductive method,we show that the generalizedμ-scrambling scrambling index of a primitive digraph D{n-t-1,n-t}.
Denote the primitive digraph with two n-t-1-cycles and one n-t-cycle by D{n-t-1,n-t}.By using the graph theory and Combining the Mathematical construction method with inductive method,we show that the generalizedμ-scrambling scrambling index of a primitive digraph D{n-t-1,n-t}.
引文
[1]Akelbek M,Kirkland S.Coefficients of ergodicity and the scrambling index[J].Linear Algebra&Its Applications,2009,430:1111-1130.
[2]Akelbek M,Kirkland S.Primitive digraphs with the largest scrambling index[J].Linear Algebra&Its Applications,2009,430:1099-1110.
[3]Cho H H,Kim S R,Nam Y.The m-step competition graph of a digraph[J].Discrete Applied Mathematics,2000,105(1/2/3):151-127.
[4]Huang Y,Liu B.Generalized scrambling indices of a primitive digraph[J].Linear Algebra&Its Applications,2010,433(11):1798-1808.
[5]Bruald R A,Liu B.Generalized exponents of primitive directed digraphs[J].Journal of Graph Theory,1990,14:483-499.
[6]Zhang L,Huang T Z.Bounds on the generalizedμ-scrambling indices of primitive digraphs[J].International Journal of Computer Mathematics,2012,89(1):17-29.
[7]Kim H K.Scrambling index set of primitive digraphs[J].Linear Algebra&Its Applications,2013,439:1886-1893.
[8]Shao Y,Shen J,Gao Y.The kth upper and lower bases of primitive nonpowerful minimally strong signed digraphs[J].Linear Multilinear Algebra,2012,60(9):1093-1113.
[9]Shao Y,Gao Y.The scrambling index set of primitive minimally strong digraphs[J].Linear Algebra&Its Applications,2016,500:1-14.
[10] Song Z,Gao Y.Scrambling index of primitive digraph with one n-cycle and two s-cycles[J].Journal of Tianjin Normal University,2016,30(1):6-11.
[2]Akelbek M,Kirkland S.Primitive digraphs with the largest scrambling index[J].Linear Algebra&Its Applications,2009,430:1099-1110.
[3]Cho H H,Kim S R,Nam Y.The m-step competition graph of a digraph[J].Discrete Applied Mathematics,2000,105(1/2/3):151-127.
[4]Huang Y,Liu B.Generalized scrambling indices of a primitive digraph[J].Linear Algebra&Its Applications,2010,433(11):1798-1808.
[5]Bruald R A,Liu B.Generalized exponents of primitive directed digraphs[J].Journal of Graph Theory,1990,14:483-499.
[6]Zhang L,Huang T Z.Bounds on the generalizedμ-scrambling indices of primitive digraphs[J].International Journal of Computer Mathematics,2012,89(1):17-29.
[7]Kim H K.Scrambling index set of primitive digraphs[J].Linear Algebra&Its Applications,2013,439:1886-1893.
[8]Shao Y,Shen J,Gao Y.The kth upper and lower bases of primitive nonpowerful minimally strong signed digraphs[J].Linear Multilinear Algebra,2012,60(9):1093-1113.
[9]Shao Y,Gao Y.The scrambling index set of primitive minimally strong digraphs[J].Linear Algebra&Its Applications,2016,500:1-14.
[10] Song Z,Gao Y.Scrambling index of primitive digraph with one n-cycle and two s-cycles[J].Journal of Tianjin Normal University,2016,30(1):6-11.