给定团数的图的距离无符号拉普拉斯谱半径

李金溪, 杨墁, 尤利华

李金溪, 杨墁, 尤利华. 给定团数的图的距离无符号拉普拉斯谱半径[J]. 华南师范大学学报(自然科学版), 2016, 48(6): 118-123.
引用本文: 李金溪, 杨墁, 尤利华. 给定团数的图的距离无符号拉普拉斯谱半径[J]. 华南师范大学学报(自然科学版), 2016, 48(6): 118-123.
The minimal distance signless Laplacian spectral radii of connected graphs with given clique number[J]. Journal of South China Normal University (Natural Science Edition), 2016, 48(6): 118-123.
Citation: The minimal distance signless Laplacian spectral radii of connected graphs with given clique number[J]. Journal of South China Normal University (Natural Science Edition), 2016, 48(6): 118-123.

给定团数的图的距离无符号拉普拉斯谱半径

基金项目: 

有限群的结构及 Fitting 类中一些问题的研究;广东省自然科学基金项目

详细信息
    通讯作者:

    尤利华

  • 中图分类号: A

The minimal distance signless Laplacian spectral radii of connected graphs with given clique number

  • 摘要: 在本文中, 我们刻画了给定团数的连通图中取得最小距离无符号拉普拉斯谱半径的极图.
    Abstract: In this paper, we characterize the extremal graph with the minimal distance signless Laplacian spectral radius among all connected graphs with given clique number.
  • [1] M. Aouchiche, P. Hansen, Two Laplacians for the distance matrix of a graph,
    Linear Algebra Appl. 439 (2013) 21-33.

    [2] J.A. Bondy, U.S.R. Murty, Graph Theory With Applications, Macmillan, Lon-
    don, 1976.

    [3] J.A. Bondy, U.S.R. Murty, Graph Theory, Springer, New York, 2008.

    [4] Abraham Berman, Robert J. Plemmons, Nonnegative Matrices in the Mathe-
    matical Sciences, New York: Academic Press, 1979.

    [5] R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University, England,
    1986.

    [6] H. Minc, Nonnegative Matrices, John Wiley and Sons Inc., New York, 1988.

    [7] J. Bang{Jensen, G. Gutin, Digraphs Theory, Algorithms and Applications,
    Springer, 2001.

    [8] R.L. Graham, L. Lovasz, Distance matrix polynomials of trees, Adv.Math 29
    (1978) 60-88.

    [9] G. Indulal, Sharp bounds on the distance spectral radius and the distance energy
    of graphs, Linear Algebra Appl. 430 (2009) 106-133.

    [10] D. Stevanovic, A. Ilic, Distance spectral radius of trees with xed maximum
    degree, Electron. J. Linear Algebra. 20 (2010) 168-179.

    [11] Z.Z. Liu, On spectral radius of the distance matrix, Appl. Anal. Discrete Math.
    4 (2010) 269-277.

    [12] X.L. Zhang, C. Godsil, Connectivity and minimal distance spectral radius of
    graphs, Linear and Multilinear Algebra 59 (2011) 745-754.

    [13] G.L. Yu, Y.R. Wu, Y.J. Zhang, J.L. Shu, Some graft transformations and its
    application on a distance spectrum, Discrete Math. 311 (2011) 2117-2123.

    [14] S.S. Bose, M. Nath, S. Paul, Distance spectral radius of graphs with r pendent
    vertices, Linear Algebra Appl. 435 (2011) 2828-2836.

    [15] G.L. Yu, H.C. Jia, H.L. Zhang, J.L. Shu, Some graft transformations and its
    applications on the distance spectral radius of a graph, Applied Mathematics
    Letters 25 (2012) 315-319.

    [16] X.L. Zhang, On the distance spectral radius of some graphs, Linear Algebra
    Appl. 437 (2012) 1930-1941.

    [17] M. Nath, S. Paul, On the distance spectral radius of bipartite graphs, Linear
    Algebra Appl. 436 (2012) 1285-1296.

    [18] M.Q. Zhai, G.L. Yu, J.L. Shu, Clique number and distance spectral radii of
    graphs, Ars Combin. 104 (2012) 385-392.

    [19] Y.N. Wang, B. Zhou, On distance spectral radius of graphs, Linear Algebra
    Appl. 438 (2013) 3490-3503.

    [20] W.J. Ning, L.Q. Ouyang, M. Lu, Distance spectral radius of trees with xed
    number of pendent vertices, Linear Algebra Appl. 439 (2013) 2240-2249.

    [21] Y.Y. Chen, H.Q. Lin, J.L. Shu, Sharp upper bounds on the distance spectral
    radius of a graph, Linear Algebra Appli. 439 (2013) 2659-2666.

    [22] H.Q. Lin, J.L. Shu, Sharp bounds on distance spectral radius of graphs, Linear
    and Multilinear Algebra 61 (2013) 442-447.

    [23] R.D. Xing, B. Zhou, J.P. Li, On the distance signless Laplacian spectral radius
    of graphs, Linear and Multilinear Algebra 62 (2014) 1377-1387.

    [24] R.D. Xing, B. Zhou, On the distance and distance signless Laplacian spectral
    radii of bicyclic graphs, Linear Algebra Appl. 439 (2013) 3955-3963.

    [25] F.L. Tian, D. Wong, J.L. Rou, Proof for four conjectures about the distance
    Laplacian and distance signless Laplacian eigenvalues of a graph, Linear Algebra
    Appl. 471 (2015) 10-20.

    [26] K.C. Das, Proof of conjectures on the distance signless Laplacian eigenvalues
    of graphs, Linear Algebra Appl. 467 (2015) 100-115.

    [27] D. Stevanovic, P. Hansen, The minimum spectral radius of graphs with a given
    clique number, Electron.J.Linear Algebra 17 (2008) 110-117.

    [28] H.Q. Lin, J.L. Shu, Y.R. Wu, G.L. Yu, Spectral radius of strongly connected
    digraphs, Discrete Math. 312 (2012) 3663-3669.

    [29] J.M. Guo, J.X. Li, W.C. Shiu, The smallest Laplacian spectral radius of graphs
    with a given clique number, Linear Algebra Appl. 437 (2012) 1109-1122.

    [30] B. He, Y.L. Jin, X.D. Zhang, Sharp bounds for the signless Laplacian spectral
    radius in terms of clique number, Linear Algebra Appl. 438 (2013) 3851-3861.

    [31] J.M. Zhang, T.Z. Huang, J.M. Guo, The smallest signless Laplacian spectral
    radius of graphs with a given clique number, Linear Algebra Appl. 439 (2013)
    2562-2576.

    [32] W.X. Hong, L.H. You, Spectral radius and signless Laplacian spectral radius
    of strongly connected digraphs, Linear Algebra Appl. 457 (2014) 93-113.

    [33] B. Bollobas, Extremal graph theory, Academic Press, London, New York, San
    Francisco, 1978.

    [34] M. Kang, O. Pikhurko, Maximum Kr+1-free graphs which are not r-partite,
    Mat. Stud. 24 (2005) 12-20.

    [1] M. Aouchiche, P. Hansen, Two Laplacians for the distance matrix of a graph,
    Linear Algebra Appl. 439 (2013) 21-33.

    [2] J.A. Bondy, U.S.R. Murty, Graph Theory With Applications, Macmillan, Lon-
    don, 1976.

    [3] J.A. Bondy, U.S.R. Murty, Graph Theory, Springer, New York, 2008.

    [4] Abraham Berman, Robert J. Plemmons, Nonnegative Matrices in the Mathe-
    matical Sciences, New York: Academic Press, 1979.

    [5] R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University, England,
    1986.

    [6] H. Minc, Nonnegative Matrices, John Wiley and Sons Inc., New York, 1988.

    [7] J. Bang{Jensen, G. Gutin, Digraphs Theory, Algorithms and Applications,
    Springer, 2001.

    [8] R.L. Graham, L. Lovasz, Distance matrix polynomials of trees, Adv.Math 29
    (1978) 60-88.

    [9] G. Indulal, Sharp bounds on the distance spectral radius and the distance energy
    of graphs, Linear Algebra Appl. 430 (2009) 106-133.

    [10] D. Stevanovic, A. Ilic, Distance spectral radius of trees with xed maximum
    degree, Electron. J. Linear Algebra. 20 (2010) 168-179.

    [11] Z.Z. Liu, On spectral radius of the distance matrix, Appl. Anal. Discrete Math.
    4 (2010) 269-277.

    [12] X.L. Zhang, C. Godsil, Connectivity and minimal distance spectral radius of
    graphs, Linear and Multilinear Algebra 59 (2011) 745-754.

    [13] G.L. Yu, Y.R. Wu, Y.J. Zhang, J.L. Shu, Some graft transformations and its
    application on a distance spectrum, Discrete Math. 311 (2011) 2117-2123.

    [14] S.S. Bose, M. Nath, S. Paul, Distance spectral radius of graphs with r pendent
    vertices, Linear Algebra Appl. 435 (2011) 2828-2836.

    [15] G.L. Yu, H.C. Jia, H.L. Zhang, J.L. Shu, Some graft transformations and its
    applications on the distance spectral radius of a graph, Applied Mathematics
    Letters 25 (2012) 315-319.

    [16] X.L. Zhang, On the distance spectral radius of some graphs, Linear Algebra
    Appl. 437 (2012) 1930-1941.

    [17] M. Nath, S. Paul, On the distance spectral radius of bipartite graphs, Linear
    Algebra Appl. 436 (2012) 1285-1296.

    [18] M.Q. Zhai, G.L. Yu, J.L. Shu, Clique number and distance spectral radii of
    graphs, Ars Combin. 104 (2012) 385-392.

    [19] Y.N. Wang, B. Zhou, On distance spectral radius of graphs, Linear Algebra
    Appl. 438 (2013) 3490-3503.

    [20] W.J. Ning, L.Q. Ouyang, M. Lu, Distance spectral radius of trees with xed
    number of pendent vertices, Linear Algebra Appl. 439 (2013) 2240-2249.

    [21] Y.Y. Chen, H.Q. Lin, J.L. Shu, Sharp upper bounds on the distance spectral
    radius of a graph, Linear Algebra Appli. 439 (2013) 2659-2666.

    [22] H.Q. Lin, J.L. Shu, Sharp bounds on distance spectral radius of graphs, Linear
    and Multilinear Algebra 61 (2013) 442-447.

    [23] R.D. Xing, B. Zhou, J.P. Li, On the distance signless Laplacian spectral radius
    of graphs, Linear and Multilinear Algebra 62 (2014) 1377-1387.

    [24] R.D. Xing, B. Zhou, On the distance and distance signless Laplacian spectral
    radii of bicyclic graphs, Linear Algebra Appl. 439 (2013) 3955-3963.

    [25] F.L. Tian, D. Wong, J.L. Rou, Proof for four conjectures about the distance
    Laplacian and distance signless Laplacian eigenvalues of a graph, Linear Algebra
    Appl. 471 (2015) 10-20.

    [26] K.C. Das, Proof of conjectures on the distance signless Laplacian eigenvalues
    of graphs, Linear Algebra Appl. 467 (2015) 100-115.

    [27] D. Stevanovic, P. Hansen, The minimum spectral radius of graphs with a given
    clique number, Electron.J.Linear Algebra 17 (2008) 110-117.

    [28] H.Q. Lin, J.L. Shu, Y.R. Wu, G.L. Yu, Spectral radius of strongly connected
    digraphs, Discrete Math. 312 (2012) 3663-3669.

    [29] J.M. Guo, J.X. Li, W.C. Shiu, The smallest Laplacian spectral radius of graphs
    with a given clique number, Linear Algebra Appl. 437 (2012) 1109-1122.

    [30] B. He, Y.L. Jin, X.D. Zhang, Sharp bounds for the signless Laplacian spectral
    radius in terms of clique number, Linear Algebra Appl. 438 (2013) 3851-3861.

    [31] J.M. Zhang, T.Z. Huang, J.M. Guo, The smallest signless Laplacian spectral
    radius of graphs with a given clique number, Linear Algebra Appl. 439 (2013)
    2562-2576.

    [32] W.X. Hong, L.H. You, Spectral radius and signless Laplacian spectral radius
    of strongly connected digraphs, Linear Algebra Appl. 457 (2014) 93-113.

    [33] B. Bollobas, Extremal graph theory, Academic Press, London, New York, San
    Francisco, 1978.

    [34] M. Kang, O. Pikhurko, Maximum Kr+1-free graphs which are not r-partite,
    Mat. Stud. 24 (2005) 12-20.

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出版历程
  • 收稿日期:  2015-11-04
  • 修回日期:  2016-02-25
  • 刊出日期:  2016-11-24

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