哈密顿图的无符号拉普拉斯谱半径条件
发布时间：2019-04-25 21:11
【摘要】：令A(G)=(a_(ij))_(n×n)是简单图G的邻接矩阵,其中若v_i-v_j,则a_(ij)=1,否则a_(ij)=0.设D(G)是度对角矩阵,其(i,i)位置是图G的顶点v_i的度.矩阵Q(G)=D(G)+A(G)表示无符号拉普拉斯矩阵.Q(G)的最大特征根称作图G的无符号拉普拉斯谱半径,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:可以通过复杂的结构分析和排除更多的例外图,当q(G)≥2n-6+4/(n-1)时,则G是哈密顿的.作为论断的有力补充,给出了图是哈密顿图的一个稍弱的充分谱条件,并给出了详细的证明和例外图.
[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，
本文编号：2465463
[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，
本文编号：2465463
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