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Minimum distance signless Laplacian spectral radius of connected graphs with cut vertices

  • 1.

    Department of Mathematics, Chizhou College, Chizhou 247000, China

  • 2.

    School of Mathematics and Computation Sciences, Anqing Normal College, Anqing 246133, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2014.12.003
  • Received Date: 22 March 2014
  • Accepted Date: 08 November 2014
  • Rev Recd Date: 08 November 2014
  • Publish Date: 30 December 2014
    Abstract

  • Abstract

    In the class of connected graphs on n vertices with cut vertices, the unique graph with minimum distance signless Laplacian spectral radius was determined by using eigenvector equation to study eigenvalues and a lower bound for the distance signless Laplacian spectral radius in terms of order n was given.

    Abstract

    In the class of connected graphs on n vertices with cut vertices, the unique graph with minimum distance signless Laplacian spectral radius was determined by using eigenvector equation to study eigenvalues and a lower bound for the distance signless Laplacian spectral radius in terms of order n was given.
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    • References(14)
  • [1]
    Guo W. The Theory of Classes of Groups [M]. Beijing/ New York: Science Press/ Kluwer Academic Publisher,2000.
    [2]
    Huppert B. Endliche Gruppen Ⅰ [M]. Berlin/ Heidelberg/ New York: Springer-Verlag, 1967.
    [3]
    Kegel O H. Sylow-Gruppen and subnormalteiler endlicher Gruppen [J]. Math Z, 1962, 78: 205-221.
    [4]
    Schmid P. Subgroups permutable with all Sylow subgroups[J]. J Algebra, 1998, 207: 285-293.
    [5]
    Wang Y. c-normality of groups and its properties[J]. J Algebra, 1996, 180: 954-965.
    [6]
    Guo X, Shum K P. On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups[J].Arch Math, 2003, 80: 561-569.
    [7]
    Ramadan M, Mohamed M E, Heliel A A. On c-normality of certain subgroups of prime power order of finite groups[J]. Arch Math, 2005, 85: 203-210.
    [8]
    Skiba A N. On weakly s-permutable subgroups of finite groups[J]. J Algebra, 2007, 315: 192-209.
    [9]
    Doerk K, Hawkes T. Finite Soluble Groups[M]. Berlin/New York: Walter de Gruyter, 1992.
    [10]
    Wielandt H. Subnormal subgroups and permutation groups [C]// Lectures given at the Ohio State University. Columbus, Ohio: Dept of Mathematics, Ohio State Univ, 1971.
    [11]
    Li Y, Wang Y, Wei H. The influence of π-quasinormality of some subgroups of a finite group[J]. Arch Math (Basel), 2003, 81: 245-252.
    [12]
    Ballester-Bolinches A, Esteban-Romero R, Asaad M. Pruducts of Finite Groups[M]. Berlin: Walter de Gruyter, 2010: 52-91.
    [13]
    Gorenstein D. Finite Groups [M]. New York: Chelsea Publishing Company, 1968.
    [14]
    Miao L. On weakly s-permutable subgroups of finite groups [J]. Bull Braz Math Soc, 2010, 41(2): 223-235.
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    [1]
    Guo W. The Theory of Classes of Groups [M]. Beijing/ New York: Science Press/ Kluwer Academic Publisher,2000.
    [2]
    Huppert B. Endliche Gruppen Ⅰ [M]. Berlin/ Heidelberg/ New York: Springer-Verlag, 1967.
    [3]
    Kegel O H. Sylow-Gruppen and subnormalteiler endlicher Gruppen [J]. Math Z, 1962, 78: 205-221.
    [4]
    Schmid P. Subgroups permutable with all Sylow subgroups[J]. J Algebra, 1998, 207: 285-293.
    [5]
    Wang Y. c-normality of groups and its properties[J]. J Algebra, 1996, 180: 954-965.
    [6]
    Guo X, Shum K P. On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups[J].Arch Math, 2003, 80: 561-569.
    [7]
    Ramadan M, Mohamed M E, Heliel A A. On c-normality of certain subgroups of prime power order of finite groups[J]. Arch Math, 2005, 85: 203-210.
    [8]
    Skiba A N. On weakly s-permutable subgroups of finite groups[J]. J Algebra, 2007, 315: 192-209.
    [9]
    Doerk K, Hawkes T. Finite Soluble Groups[M]. Berlin/New York: Walter de Gruyter, 1992.
    [10]
    Wielandt H. Subnormal subgroups and permutation groups [C]// Lectures given at the Ohio State University. Columbus, Ohio: Dept of Mathematics, Ohio State Univ, 1971.
    [11]
    Li Y, Wang Y, Wei H. The influence of π-quasinormality of some subgroups of a finite group[J]. Arch Math (Basel), 2003, 81: 245-252.
    [12]
    Ballester-Bolinches A, Esteban-Romero R, Asaad M. Pruducts of Finite Groups[M]. Berlin: Walter de Gruyter, 2010: 52-91.
    [13]
    Gorenstein D. Finite Groups [M]. New York: Chelsea Publishing Company, 1968.
    [14]
    Miao L. On weakly s-permutable subgroups of finite groups [J]. Bull Braz Math Soc, 2010, 41(2): 223-235.
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