Graph Theory

A branch of math in which graphs are used to solve a problem. It is unlike a Cartesian graph that we used throughout our younger years of math. Here it is a collection of line segments and points (nodes). These nodes have been called vertices in the past and the line segments, edges. Networks can illustrate this relationship among a variety of objects or sets.

Adjacent – two vertices connected by an edge are termed adjacent. Degree of the vertex – the number of edges that begin or end at a vertex. A loop counts as two degrees. Path – connected sequence of vertices Circuit – when a path begins and ends at the same vertex. A circuit depends on the route taken.

Networks Connected – if and only if there is at least one path connecting each pair of vertices. Complete – has an edge between every pair of vertices. Traceable – all vertices are connected to at least one other vertex and all edges can be traveled exactly once in a continuous path. A network is traceable if it has only vertices of even degree or exactly two vertices of odd degree.

Planar – a network can be drawn on a two dimensional surface so that edges do not cross anywhere except at vertices. Homework Pg 49 # 1,3,5,6,7, 8, 9, 10, 11,15, 21