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

Ming-Zhu Chen and Xiao-Dong Zhang ()
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Ming-Zhu Chen: Shanghai Jiao Tong University
Xiao-Dong Zhang: Shanghai Jiao Tong University

Journal of Combinatorial Optimization, 2018, vol. 35, issue 4, No 6, 1104-1127

Abstract: 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.

Keywords: Hamilton-connected; Minimum degree; The number of edges; Spectral radius; Signless Laplacian spectral radius; 05C50; 05C35 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-018-0260-3

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