The number of edges,spectral radius and Hamilton-connectedness of graphs |
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Authors: | Ming-Zhu Chen Xiao-Dong Zhang |
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Institution: | 1.School of Mathematical Sciences, MOE-LSC, SHL-MAC,Shanghai Jiao Tong University,Shanghai,People’s Republic of China |
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Abstract: | In this paper, we prove that a simple graph G of order sufficiently large n with the minimal degree \(\delta (G)\ge k\ge 2\) is Hamilton-connected except for two classes of graphs if the number of edges in G is at least \(\frac{1}{2}(n^2-(2k-1)n + 2k-2)\). 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. |
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