Graph Theory is the study of interactions between nodes (vertices) and edges (connections between the vertices), and it relates to topics such as combinatorics, scheduling, and connectivity making it useful to computer science and programming, engineering, networks and relationships, and many other fields of science. Graph theory can be thought of as the "mathematician's connectthedots" but it does not examine graphs as done in Calculus (curves and other related concepts).
Table of Chapters

Simple Tools
 Juggling with Binomial Coefficients
 Dual Graphs
 StarDelta and Similar Transformations
 Hypercubes and Gray Codes
Degrees and Parameters
 Degree Definitions
 Theorems using Degrees
 Regular Graphs
 Degree Sequences
 Using matrices to encode graphs
Special Types of Graphs
 kConnected Graphs
 Planar Graphs