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

The Signless Laplacian Spectral Radius with Given Independence Number

Author LiRuiLin
Tutor ShiJinSong
School East China University of Science and Technology
Course Applied Mathematics
Keywords Laplacian spectrum Spectral radius The number of independent Bicyclic Graphs
CLC O157.5
Type Master's thesis
Year 2011
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Atlas theory is an important part of the graph theory , which includes adjacent spectral theory , Laplace spectral theory , intended to Laplace spectral theory . In these spectra with Laplacian spectrum reflect the nature and structure of the Figure is the most convenient. S is a graph G is a set of ideas , if any two points in S are not adjacent , then S is an independent set . Independent set of maximum cardinality is called the independence number of a graph G , denoted by alpha ( G ) . | E ( G ) | = | V ( G ) │ connected graph G said bicyclic graphs . Hutchison order n , the number of independent alpha double circle picture shows ( ? ) ( N , alpha ) , ( ? ) 1 ( n , alpha ) ( ? ) ( N , alpha ) with two edge disjoint ring bicyclic graphs ( ? ) 2 ( n , a ) = ( ? ) ( n , alpha ) \\ ( ? ) 1 ( n alpha ) . In this paper, the Laplacian spectra of the structure and properties of a given number of independent . Firstly, the Laplacian spectral radius sector and Laplacian spectral radius of the given parameter pole figure depicts the results . Second , we characterize the n-order simple connected graph , independence number a ( G ) ∈ {1,2 , [ n / 2 ] , [ n / 2 ] 1 , n -3 , n - 2 , n - 1 } with the smallest Laplacian spectral radius of the pole figure . Finally , for any number of independent alpha were portrayed ( ? ) With the largest Laplacian spectral radius of the pole figure 1 ( n , alpha ) , ( ? ) 2 ( n , alpha ) , and further ( ? ) ( n , alpha ) Laplacian spectral radius of the sector and the pole figure .

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