Spectral radius and Hamiltonicity of graphs |
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Authors: | Miroslav Fiedler |
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Institution: | a Department of Computational Methods, Institute of Computer Science, Academy of Sciences of the Czech Republic, Czech Republic b Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA |
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Abstract: | Let G be a graph of order n and μ(G) be the largest eigenvalue of its adjacency matrix. Let be the complement of G.Write Kn-1+v for the complete graph on n-1 vertices together with an isolated vertex, and Kn-1+e for the complete graph on n-1 vertices with a pendent edge.We show that:If μ(G)?n-2, then G contains a Hamiltonian path unless G=Kn-1+v; if strict inequality holds, then G contains a Hamiltonian cycle unless G=Kn-1+e.If , then G contains a Hamiltonian path unless G=Kn-1+v.If , then G contains a Hamiltonian cycle unless G=Kn-1+e. |
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Keywords: | 05C50 05C35 |
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