Introduction to Graphs
Gary Chartrand, Ping Zhang · 2019
This chapter describes some of the fundamental concepts and theorems encountered in the investigation of graph colorings as well as some common terminology and notation in graph theory. Graphs are typically represented by diagrams in which each vertex is represented by a point or small circle (open or solid) and each edge is represented by a line segment or curve joining the corresponding small circles. A well-known theorem in graph theory deals with the sum of the degrees of the vertices of a graph. This theorem was indirectly observed by the great Swiss mathematician Leonhard Euler. It is often referred to as the First Theorem of Graph Theory. The chapter discusses isomorphic graphs, non-isomorphic graphs, and some common graphs that are encountered so frequently.