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Graph Theory Lecture Notes

Graph Theory : Penn State Math 485 LectureNotesVersion Griffin 2011-2021 Licensed under a Creative Commons Attribution-Noncommercial-Share Alike United States LicenseWith Contributions By:Elena KosyginaSuraj ShekharContentsList of FiguresvPrefacexiChapter 1. Introduction to Graph Theory11. An Overview of Graph Theory12. Graphs, Multi-Graphs, Simple Graphs23. Directed Graphs74. Elementary Graph Properties: Degrees and Degree Sequences95. Subgraphs146. Graph Complement, Cliques and Independent Sets15 Chapter 2. More Definitions and Theorems191. Paths, Walks, and Cycles192. More Graph Properties: Diameter, Radius, Circumference, Girth213. More on Trails and Cycles224. Graph Components235. Introduction to Centrality286. Bipartite Graphs297. Acyclic Graphs and Trees31 Chapter 3. Trees, Algorithms and Matroids391.

Chapter 4. Some Algebraic Graph Theory65 1. Isomorphism and Automorphism65 2. Fields and Matrices71 3. Special Matrices and Vectors73 4. Matrix Representations of Graphs73 5. Determinants, Eigenvalue and Eigenvectors76 6. Properties of the Eigenvalues of the Adjacency Matrix79 Chapter 5. Applications of Algebraic Graph Theory83 iii

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