Characterization of bipartite graph with maximum spectral radius
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摘要: 一个图G的邻接矩阵A(G)是n\times n矩阵,如果v_i和v_j相邻, 那么它的(i,j)位置为1, 否则为0. 图G的谱半径是邻接矩阵A(G)的最大特征值. 本文确定了在所有的树和所有的二部单圈图、二部双圈图、二部三圈图、二部四圈图、二部五圈 图以及二部拟树图中 所对应的具有最大谱半径的图.Abstract: The adjacency matrix A(G) of a graph G is the n\times n matrix with its (i,j)-entry equal to 1 if v_i and v_j are adjacent, and 0 otherwise. The spectral radius of G is the largest eigenvalue of A(G). In this paper we determine the graphs with maximum spectral radius among all trees, and all bipartite unicyclic, bicyclic, tricyclic, tetracyclic, pentacyclic and quasi-tree graphs, respectively.
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Key words:
- bipartite graph cyclespectral radius /
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[1] [1]BERMAN A, ZHANG X D. On the spectral radius of graph with cut vertices [J]. J Combin Theory Ser B, 2001, 83: 233-240.[2] BRUALDI R, SOLHEID E. On the spectral radius of connected graphs[J]. Publ Inst Math (Beograd), 1986, 39 (53): 45-53.[3]HOU Y P, LI J S. Bounds on the largest eigenvalues of trees with a given size of matching [J]. Linear Algebra Appl, 2002, 342: 203-217.
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