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The Graphs of Diameter n-4 with the Second Smallest Spectral Radius

Author: JiangJingJing
Tutor: TanShangWang
School: China University of Petroleum
Course: Mathematics
Keywords: Map Tree The minimum spectral radius Sequencing Diameter
CLC: O157.5
Type: Master's thesis
Year: 2011
Downloads: 8
Quote: 0
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Abstract


Atlas theory is an important research topic of algebraic graph theory , which includes the adjacency spectrum and the Laplace spectrum . Fig tree is a very special and important , precisely because of the nature of the characteristic of the tree , so many communicating FIG tend to be by means of the characteristics of the tree to be . This paper will examine the adjacency spectrum . The maximum spectral radius of the graph sequencing have been many good conclusion , but the minimum spectral radius of sequencing the conclusion is relatively small . This paper has drawn a conclusion on the basis of further determine the number of vertices is n and the diameter D ∈ n - 2 , n - 3 , n - 4 's all connected graph spectral radius connected graph . The main content of this paper is divided into three parts: 1 . Map theory an overview of the total , introduces the concepts and notation of the map , and the text of the structural description . Chapter 2 First n-2 tree diameter for the relatively simple sequencer ; then the n-3 and n-4 of the diameter of the tree classification, to study the nature of each category tree , in accordance with the smallest spectral radius of the tree sequencing and identify the spectral radius of each type of tree small tree . Chapter 3 is that the diameter for the n - 2 , n - 3 , n -4 n - connected graph of order , the spectral radius map will be as a tree .

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