A graph G possesses Hamiltonian s-properties when G is Hamilton-connected if s=1,Hamiltonian if s=0,and traceable if s=-1.Let S_A(G)=λ_n(G)-λ_1(G)and S_L(G)=μ_n(G)-μ_2(G)be the spread and the Laplacian spread of G...A graph G possesses Hamiltonian s-properties when G is Hamilton-connected if s=1,Hamiltonian if s=0,and traceable if s=-1.Let S_A(G)=λ_n(G)-λ_1(G)and S_L(G)=μ_n(G)-μ_2(G)be the spread and the Laplacian spread of G,respectively,whereλ_n(G)andλ_1(G)are the largest and smallest eigenvalues of G,andμ_n(G)andμ_2(G)are the largest and second smallest Laplacian eigenvalues of G,respectively.In this paper,we shall present two sufficient conditions involving S_A(G)and S_L(G)for a k-connected graph to possess Hamiltonian s-properties,respectively.We also derive a sufficient condition on the Laplacian eigenratio μ2(G)/μ(G) for a k-connected graph to possess Hamiltonian s-properties.展开更多
基金Supported by NSFC(Nos.12171089,12271235)NSF of Fujian Province(No.2021J02048)。
文摘A graph G possesses Hamiltonian s-properties when G is Hamilton-connected if s=1,Hamiltonian if s=0,and traceable if s=-1.Let S_A(G)=λ_n(G)-λ_1(G)and S_L(G)=μ_n(G)-μ_2(G)be the spread and the Laplacian spread of G,respectively,whereλ_n(G)andλ_1(G)are the largest and smallest eigenvalues of G,andμ_n(G)andμ_2(G)are the largest and second smallest Laplacian eigenvalues of G,respectively.In this paper,we shall present two sufficient conditions involving S_A(G)and S_L(G)for a k-connected graph to possess Hamiltonian s-properties,respectively.We also derive a sufficient condition on the Laplacian eigenratio μ2(G)/μ(G) for a k-connected graph to possess Hamiltonian s-properties.
