圖論基礎(chǔ)

內(nèi)容概要

張海良、蘇岐芳、林榮斐編著的《圖論基礎(chǔ)》除了介紹圖論的基本概念和簡單結(jié)構(gòu)理論外，主要研究總結(jié)了近些年來比較熱門的關(guān)于圖的鄰接譜、圖的匹配多項式、圖的著色、圖的色多項式、圖的拉普拉斯多項式和圖的準(zhǔn)拉普拉斯多項式的一些主要成果。為了方便讀者進(jìn)行研究和參考，我們也采編了一些和圖論問題相關(guān)的線性代數(shù)、矩陣論的理論知識。在書的后面給出了基本符號及中英文對照表，以方便讀者查閱參考。
《圖論基礎(chǔ)》內(nèi)容詳細(xì)，證明簡潔，并且在每章后面提供了一些新的研究內(nèi)容與素材并配以一定量的習(xí)題，可作為數(shù)學(xué)與應(yīng)用數(shù)學(xué)專業(yè)高年級的專業(yè)選修課和圖論方向的一年級的碩士研究生課程的教材，也可作為廣大圖論研究工作者的參考用書。

書籍目錄

Preface in Chinese
Chapter 1 Basic concepts
  1.1 Graph and simple graph
  1.2 Graph operations
  1.3 Isomorphism
  1.4 Incident and adjacent matrix
  1.5 The spectrum of graph
  1.6 The spectrum of several graphs
  1.7 Results from matrix theory
  1.8 About the largest zero of characteristic polynomials
  1.9 Spectrum radius
Chapter 2 path and cycle
  2.1 The path
  2.2 The cycle
  2.3 The diameter of a graph and its complement graph
Chapter 3 Tree
  3.1 Tree
  3.2 Spanning tree
  3.3 A bound for the tree number of regular graphs
  3.4 Cycle space and bound space of a graph
Chapter 4 Connectivity
  4.1 Cut edges
  4.2 Cut vertex
  4.3 Block
  4.4 Connectivity
Chapter 5 Euler and Hamilton graphs
  5.1 Euler path and circuits
  5.2 Hamilton graph
Chapter 6 Matching and matching polynomial
  6.1 Matching
  6.2 Bipartite graph and perfect matching
  6.3 Matching polynomial
  6.4 The relation between spectrum and matching polynomial
  6.5 Relation between several graphs
  6.6 Several matching equivalent and matching unique graphs
  6.7 The Hosoya index of several graphs
  6.8 Two trees with minimal Hosoya index
  6.9 Recent results in matching
Chapter 7 Laplacian and Quasi-Laplacian spectrum
  7.1 Sigma function
  7.2 The spanning tree and sigma function
  7.3 Quasi-Laplacian Spectrum
  7.4 Basic lemmas
  7.5 Main results
  7.6 Three different spectrum of regular graphs
Chapter 8 More theorems form matrix theory
  8.1 The irreducible matrix
  8.2 Cauchy's interlacing theorem
  8.3 The eigenvalues of A（G） and graph structure
Chapter 9 Chromatic polynomial
  9.1 Induction
  9.2 Two different formula for chromatic polynomial
  9.3 Chromatic polynomials for several type of graphs
  9.4 Estimate the color number
References
Bibliography

編輯推薦

　　《圖論基礎(chǔ)》的特點：內(nèi)容基礎(chǔ)、簡單易于初學(xué)者掌握。主要側(cè)重圖基本結(jié)構(gòu)與圖的譜理論的相互關(guān)系.另外對多項式理論也進(jìn)行了討論。內(nèi)容新穎，尤其是圖的匹配多項式方面介紹了近年來的最新研究成果。采用英語語言編寫，可以作為雙語教材。

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