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# CaGe V0.3

### Introduction

CaGe (**Ca**rbon **Ge**nerator) is a computer program which takes the output of
some graph generation program as input and provides several output
styles, especially graphical output. Windows, buttons etc. are used to
interact with CaGe. CaGe is based on Tcl/Tk and
thus behaves like typical Tcl/Tk--applications. Since the generated graphs
can be interpreted as molecules, CaGe is interesting not only for
graph theorists, but especially for chemists.

Since chemists use a rather different terminology than graph theorists, here
is a short list of correspondences: An **atom** in chemistry is
represented by a **vertex** in graph theory. The same way, a
**bond**
between two atoms is represented by an **edge**.
A double or triple bond is only represented by a single edge. A vertex is
**adjacent** to another vertex if they are connected by an edge.
So, if two vertices are adjacent to each other, this means that (considered
as atoms) they have bonds. The **valence** of a vertex is the
number of
adjacent vertices. Since the vertex is interpreted as an atom, it is the
number of other atoms it has bonds with, but not the number of bonds itself.
E.g. for a carbon atom, the valence is
**not** always 4: Double bonds are considered as one adjacency.

A **graph** (sometimes a graph is also called **map**)
corresponds to a **molecule**. A graph is
**x--regular** if every vertex is x--valent. So this means that
every atom has bonds to exactly x other atoms.