【摘要】：令A(G)=(a_(ij))_(n×n)是簡單圖G的鄰接矩陣,其中若v_i-v_j,則a_(ij)=1,否則a_(ij)=0.設D(G)是度對角矩陣,其(i,i)位置是圖G的頂點v_i的度.矩陣Q(G)=D(G)+A(G)表示無符號拉普拉斯矩陣.Q(G)的最大特征根稱作圖G的無符號拉普拉斯譜半徑,用q(G)表示.Liu,Shiu and Xue[R.Liu,W.Shui,J.Xue,Sufficient spectral conditions on Hamiltonian and traceable graphs,Linear Algebra Appl.467(2015)254-255]指出:可以通過復雜的結構分析和排除更多的例外圖,當q(G)≥2n-6+4/(n-1)時,則G是哈密頓的.作為論斷的有力補充,給出了圖是哈密頓圖的一個稍弱的充分譜條件,并給出了詳細的證明和例外圖.
[Abstract]:Let A (G) = (a _ (ij) _ (n 脳 n) be an adjacency matrix of a simple graph G, where a _ (ij) = 1 if v _ (ij) _ (n 脳 n), otherwise a _ (ij) = 0. Let D (G) be a degree diagonal matrix, and its (I, I) position is the degree of the vertex of graph G. The matrix Q (G) = D (G) A (G) denotes the unsigned Laplacian matrix. The largest eigenvalue of Q (G) is called the unsigned Laplace spectral radius of graph G. it is represented by q (G). Liu, Shiu and Xue [R. Liu, W. Shui, J. Xue, Sufficient spectral conditions on Hamiltonian and traceable graphs,Linear Algebra Appl.467 (2015) 254 / 255 points out that G is Hamiltonian when q (G) 鈮，

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