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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.

1.3 A self-loop is an edge in a graph Gthat contains exactly one vertex. That is, an edge that is a one element subset of the vertex set. Self-loops are illustrated by loops at the vertex in question.4 1.4 Representing each island as a dot and each bridge as a line or curve connecting

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