Spectral radius and Hamiltonicity of graphs with large minimum degree

By Vladimir Nikiforov. Czechoslovak Mathematical Journal, 2016

47 citations recorded by the source corpus.

Let G be a graph of order n and λ(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 ≥ 2, n ≥ k3 + k + 4, and let G be a graph of order n, with minimum degree δ(G) ≥ k. If λ(G)≥n−k−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda \left( G \right) \geqslant n - k - 1$$\end{document} , then G has a Hamiltonian cycle, unless G = K1∨(Kn−k−1+Kk) or G = Kk∨(Kn−2k+ K¯k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar K_k}$$\end{document} ).

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/66ef59ea529a86efc7866e37c02dc0f08e96ad57

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In Computational Theory and Mathematics

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