Spectral radius and Hamiltonicity of graphs with large minimum degree

Czechoslovak Mathematical Journal

Vladimir Nikiforov¹ 

[1] Department of Mathematical Sciences, University of Memphis, 3720 Alumni Ave, Memphis, 38152, Tennessee, USA

关键词: Hamiltonian cycle;    Hamiltonian path;    minimum degree;    spectral radius;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

Let $G$ be a graph of order $n$ and $\lambda( G) $ the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in $G$. One of the main results of the paper is the following theorem:Let $k\geq2,$ $n\geq k^3+k+4,$ and let $G$ be a graph of order $n$, with minimum degree $\delta(G) \geq k.$ If \lambda( G) \geq n-k-1, then $G$ has a Hamiltonian cycle, unless $G=K_1\vee(K_{n-k-1}+K_k)$ or $G=K_k\vee(K_{n-2k}+\bar{K}_k).$

【 授权许可】

Unknown