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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. Two Tree Search Algorithms392. Prim s Spanning Tree Algorithm413.

1.14 A graph and its complement with cliques in one illustrated and independent sets in the other illustrated.17 1.15 A covering is a set of vertices so that ever edge has at least one endpoint inside the covering set.17 2.1 A walk (a), cycle (b), Eulerian trail (c) and Hamiltonian path (d) are illustrated.20 2.2 We illustrate the 6-cycle and 4 ...

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