The Spectral Characterization of Hamiltonicity of Graphs
Volume 5 - Issue 2
Guidong Yu1,2* and Gaixiang Cai1
- 1School of Mathmatics and Physic, Anqing Normal University, China
- 2Department of Public Teanching, Hefei Preschool Education College, China
Received:September 13, 2021 Published: September 29, 2021
Corresponding author: Guidong Yu, School of Mathmatics and Physic, Anqing Normal University, Anqing 246133, Department of Public Teanching, Hefei Preschool Education College, Hefei 230013, China
DOI: 10.32474/JAAS.2021.05.000209
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Abstract
It is an important NP-complete problem in structure graph theory to judge whether a graph is Hamiltonian. So far, there is no perfect description on this problem. Therefore, it has always been concerned by the workers of graph theory and mathematics. It is explored that the new method for characterization of Hamiltonicity of graphs. Because the spectrum of a graph can well reflect the structural properties of a graph and is easy to calculate, at the 2010 conference of the theory of graph spectra, M. Fiedler and V. Nikiforov formally proposed whether the theory of graph spectra can be used to study the Hamiltonicity of a graph, and they [1] gave sufficient conditions for given graph to be Hamiltonian (or traceable) in terms of the spectral radius of the graph.
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