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Sufficient conditions for a graph to be Hamilton-connected and traceable from every vertex

Funds:  Supported by Natural Science Foundation of Anhui Province (1808085MA04), Natural Science Foundation of Department of Education of Anhui Province (KJ2017A362).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.02.003
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  • Author Bio:

    WANG Lixiang, female, born in 1980, master/lecturer.Research field: Graphing & optimal grouping.E-mail: lixiangwang2006@163.com

  • Corresponding author: YU Guidong
  • Received Date: 03 September 2018
  • Accepted Date: 06 November 2018
  • Rev Recd Date: 06 November 2018
  • Publish Date: 28 February 2020
    Abstract

  • Abstract

    A path passing through all the vertices of

    Abstract

    A path passing through all the vertices of
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    • References(8)
  • [1]
    YU G D, FAN Y Z.Spectral conditions for a graph to be Hamilton-connected[J].Applied Mechanics and Materials, 2013, 336-338: 2329-2334.
    [2]
    HO T Y, LIN C K, TAN J J M, et al.On the extremal number of edges in Hamiltonian connected graphs[J].Applied Mechanics Letters, 2010, 23(1): 26-29.
    [3]
    ZHOU Q N, WANG L G.Some sufficient spectral conditions on Hamilton-connected and traceable graphs[J].Linear Multilinear Algebra, 2017, 65(2): 224-234.
    [4]
    CHEN M Z, ZHANG X D.The number of edges, spectral radius and Hamilton-connectedness of graphs[J].Journal of Combinatorial Optimization, 2018, 35: 1104-1127.
    [5]
    BERGE C. Graphs and Hypergraphs[M]. Translated by MINIEKA E. Amsterdam: North-Holland, 1973.
    [6]
    BONDY J A, MURTY U S R. Graph Theory[M]. New York: Springer, 2008.
    [7]
    NIKIFOROV V. Some inequalities for the largest eigenvalue of a graph[J]. Combinatorics Probability and Computing, 2002, 11: 179-189.
    [8]
    FENG L H, YU G H. On three conjectures involving the signless Laplacian spectral radius of graphs[J].Publications de l Institut Mathematique, 2009, 99: 35-38.)
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    [1]
    YU G D, FAN Y Z.Spectral conditions for a graph to be Hamilton-connected[J].Applied Mechanics and Materials, 2013, 336-338: 2329-2334.
    [2]
    HO T Y, LIN C K, TAN J J M, et al.On the extremal number of edges in Hamiltonian connected graphs[J].Applied Mechanics Letters, 2010, 23(1): 26-29.
    [3]
    ZHOU Q N, WANG L G.Some sufficient spectral conditions on Hamilton-connected and traceable graphs[J].Linear Multilinear Algebra, 2017, 65(2): 224-234.
    [4]
    CHEN M Z, ZHANG X D.The number of edges, spectral radius and Hamilton-connectedness of graphs[J].Journal of Combinatorial Optimization, 2018, 35: 1104-1127.
    [5]
    BERGE C. Graphs and Hypergraphs[M]. Translated by MINIEKA E. Amsterdam: North-Holland, 1973.
    [6]
    BONDY J A, MURTY U S R. Graph Theory[M]. New York: Springer, 2008.
    [7]
    NIKIFOROV V. Some inequalities for the largest eigenvalue of a graph[J]. Combinatorics Probability and Computing, 2002, 11: 179-189.
    [8]
    FENG L H, YU G H. On three conjectures involving the signless Laplacian spectral radius of graphs[J].Publications de l Institut Mathematique, 2009, 99: 35-38.)
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