Spectral analogues of Erdős’ theorem on Hamilton-connected graphs

Jia Wei, Zhifu You and Hong-Jian Lai

Applied Mathematics and Computation, 2019, vol. 340, issue C, 242-250

Abstract: A graph G is Hamilton-connected if for any pair of vertices v and w, G has a spanning (v, w)-path. Extending theorems of Dirac and Ore, Erdős prove a sufficient condition in terms of minimum degree and the size of G to assure G to be Hamiltonian. We investigate the spectral analogous of Erdős’ theorem for a Hamilton-connected graph with given minimum degree, and prove that there exist two graphs {Lnk,Mnk} such that each of the following holds for an integer k ≥ 3 and a simple graph G on n vertices.

Keywords: Spectral radius; Hamilton-connected; Minimum degree (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:340:y:2019:i:c:p:242-250

DOI: 10.1016/j.amc.2018.08.005

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