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The maximum signless Laplacian separator of tricyclic and quadricyclic graphs

  • School of Science, North University of China, Taiyuan 030051,China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.04.003
  • Received Date: 06 August 2019
  • Accepted Date: 10 January 2020
  • Rev Recd Date: 10 January 2020
  • Publish Date: 30 April 2020
    Abstract

  • Abstract

    Let G be a graphs of order n and q1(G)≥q2(G)≥…≥qn(G) be its Q-eigenvalues. The signless Laplacian separator SQ(G) of G is defined as SQ(G)=q1(G)-q2(G). The maximum signless Laplacian separator of tricyclic and quadricyclic graphs was studied, and the corresponding extremal graphs were characterized.

    Abstract

    Let G be a graphs of order n and q1(G)≥q2(G)≥…≥qn(G) be its Q-eigenvalues. The signless Laplacian separator SQ(G) of G is defined as SQ(G)=q1(G)-q2(G). The maximum signless Laplacian separator of tricyclic and quadricyclic graphs was studied, and the corresponding extremal graphs were characterized.
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    • References(8)
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    王树禾. 图论及其应用[M].2版.北京：科学出版社，2004.
    [2]
    王朝瑞.图论[M].3版.北京：北京理工大学出版社，2001.
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    余桂东,黄冬明,张午骁,等. 双圈图和三圈图的最大拉普拉斯分离度[J]. 中国科学技术大学学报，2017,47(9):733-737.
    YU Guidong, HUANG Dongming, ZHANG Wuxiao, et al.The maximum Laplacian separators of bicyclic and tricyclic graphs[J]. Journal of University of Science and Technology of China, 2017, 47(9): 733-737.
    [4]
    简相国，袁西英，张曼. 单圈图和双圈图的最大无符号拉普拉斯分离度[J]. 运筹学学报,2015,19(2):99-104.
    JIAN Xiangguo, YUAN Xiying, ZHANG Man. The maximum signless Laplacian separator of unicyclic and bicyclic graphs[J]. Operations Research Transactions, 2015, 19(2): 99-104.
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    陈媛媛,牟善志,王国平. 一些图的无符号拉普拉斯半径[J]. 华东师范大学学报（自然科学版）,2017,6(1): 26-31.
    CHEN Yuanyuan, MU Shanzhi, WANG Guoping. On the signless Laplacian spectral radius of some graphs[J]. Journal of East China Normal University (Natural Science), 2017, 6(1): 26-31.
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    HEUVEL J V D. Hamilton cycles and eigenvalues of graphs[J]. Linear Algebra and Its Application, 1995, 226-228: 723-730.
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    MERRIS R. A note on Laplacian graph eigenvalues[J]. Linear Algebra Appl,1998, 285: 33-35.
    [8]
    YUAN X Y. A note on Laplacian spectral radii of bicyclic graphs[J]. Advances in Mathematics, 2010, 39(6): 703-708.)
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    [1]
    王树禾. 图论及其应用[M].2版.北京：科学出版社，2004.
    [2]
    王朝瑞.图论[M].3版.北京：北京理工大学出版社，2001.
    [3]
    余桂东,黄冬明,张午骁,等. 双圈图和三圈图的最大拉普拉斯分离度[J]. 中国科学技术大学学报，2017,47(9):733-737.
    YU Guidong, HUANG Dongming, ZHANG Wuxiao, et al.The maximum Laplacian separators of bicyclic and tricyclic graphs[J]. Journal of University of Science and Technology of China, 2017, 47(9): 733-737.
    [4]
    简相国，袁西英，张曼. 单圈图和双圈图的最大无符号拉普拉斯分离度[J]. 运筹学学报,2015,19(2):99-104.
    JIAN Xiangguo, YUAN Xiying, ZHANG Man. The maximum signless Laplacian separator of unicyclic and bicyclic graphs[J]. Operations Research Transactions, 2015, 19(2): 99-104.
    [5]
    陈媛媛,牟善志,王国平. 一些图的无符号拉普拉斯半径[J]. 华东师范大学学报（自然科学版）,2017,6(1): 26-31.
    CHEN Yuanyuan, MU Shanzhi, WANG Guoping. On the signless Laplacian spectral radius of some graphs[J]. Journal of East China Normal University (Natural Science), 2017, 6(1): 26-31.
    [6]
    HEUVEL J V D. Hamilton cycles and eigenvalues of graphs[J]. Linear Algebra and Its Application, 1995, 226-228: 723-730.
    [7]
    MERRIS R. A note on Laplacian graph eigenvalues[J]. Linear Algebra Appl,1998, 285: 33-35.
    [8]
    YUAN X Y. A note on Laplacian spectral radii of bicyclic graphs[J]. Advances in Mathematics, 2010, 39(6): 703-708.)
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