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The number of edges, spectral radius and Hamilton-connectedness of graphs

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  • Ming-Zhu Chen

    (Shanghai Jiao Tong University)

  • Xiao-Dong Zhang

    (Shanghai Jiao Tong University)

Abstract

In this paper, we prove that a simple graph G of order sufficiently large n with the minimal degree $$\delta (G)\ge k\ge 2$$ δ ( G ) ≥ k ≥ 2 is Hamilton-connected except for two classes of graphs if the number of edges in G is at least $$\frac{1}{2}(n^2-(2k-1)n + 2k-2)$$ 1 2 ( n 2 - ( 2 k - 1 ) n + 2 k - 2 ) . In addition, this result is used to present sufficient spectral conditions for a graph with large minimum degree to be Hamilton-connected in terms of spectral radius or signless Laplacian spectral radius, which extends the results of (Zhou and Wang in Linear Multilinear Algebra 65(2):224–234, 2017) for sufficiently large n. Moreover, we also give a sufficient spectral condition for a graph with large minimum degree to be Hamilton-connected in terms of spectral radius of its complement graph.

Suggested Citation

  • Ming-Zhu Chen & Xiao-Dong Zhang, 2018. "The number of edges, spectral radius and Hamilton-connectedness of graphs," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1104-1127, May.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:4:d:10.1007_s10878-018-0260-3
    DOI: 10.1007/s10878-018-0260-3
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    References listed on IDEAS

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    1. Guidong Yu & Miaolin Ye & Gaixiang Cai & Jinde Cao, 2014. "Signless Laplacian Spectral Conditions for Hamiltonicity of Graphs," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, June.
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    Cited by:

    1. Wei, Jia & You, Zhifu & Lai, Hong-Jian, 2019. "Spectral analogues of Erdős’ theorem on Hamilton-connected graphs," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 242-250.

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