Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Combinatorics ( combinatorics ) > Graph Theory

Bicyclic Graphs with Exactly Two Main Eigenvalues

Author ZhuChunFeng
Tutor HuZhiQuan
School Central China Normal University
Course Operational Research and Cybernetics
Keywords Map Principal eigenvalue Bicyclic Graphs The degree of linear graph
CLC O157.5
Type Master's thesis
Year 2009
Downloads 31
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Let G = ( V , E ) is a simple connected graph , where V = { v 1 < / sub > the v 2 < / sub > , ... , the v n < / sub > } set of vertices , E is the set of edges . G adjacency matrix A = ( a ij < / sub > ) n × n < / sub > , a ij connection point v i < / sub > the v j < / sub > of the number of edges . The eigenvalues ??and eigenvectors of A (G) are called the eigenvalues ??and eigenvectors of a graph G . G FIG one characteristic value is called the principal eigenvalue , if G is the characteristic vector corresponding to the feature value of each component and is not zero . The largest eigenvalue of the graph G ( spectrum root ) is always the value of its main characteristics . FIG main characteristic value plays a very important role in Spectrum Theory and Its Applications . Known graph G has exactly one main characteristic value if and only if it is a regular graph . In [ 11 ] , Hou and Tian portrayed exactly two main eigenvalues ??Unicyclicgraph portrayed all bicyclic graphs with exactly two main eigenvalues ??.

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