~Hit <space> for more help

      How to navigate around the help system

   The structure of the help system parallels that of
EG itself, that is, the menus and submenus of the help
system correspond to the control menus.

   The help system is structured like a tree  (if you
are just starting out in graph theory, think of a real
tree...).  Help text is available at every node of the
tree, not just at the leaves.

   To read the text at a particular node, highlight
the entry in the help menu and hit <space>.  (That's
what you did to get here.)

   Every node in the help system has text attached, so
you can always hit <space> and find something to read.
Not all nodes have further menus beyond them; those
that do are indicated with an ellipsis, thus:  ...

   To see the help menu options beyond a particular
node, highlight that node and hit <enter>.

   To get out of a help menu, hit <esc>.  This will
return you to the previous menu, so if you are several
menus down in the hierarchy, you will have to hit
<esc> several times.

   In general, it is probably a good idea to read the
text associated with a particular node before going on
to nodes further down the tree.

   If you are just starting with EG, you probably ought
to read the help screen "About the Main Menu" next.
After that, you should read the help screen "Getting
OUT".

~About the Main Menu

                 Main Menu

   The main menu looks like this:

F1 help
Delete
Edit
Files
New
Precis
Read
Seed
Write
eXit
Z-special
-> right
<- left


   The options available fall into several categories,
and the help system is divided into those categories
as described below:

  help category                   describes
  -------------                   ---------

  Graph Files                     Read
                                  Write
                                  Files

  Editing Graphs                  Edit
                                  Precis

  Creating Graphs                 New

  The Graph Stack                 -> right
                                  <- left
                                  Delete

  Getting OUT                     eXit

  Miscellany                      Seed
                                  Z-special

~Menu items & hotkeys

   There are two ways to activate a menu item:  either
use the up/down arrow keys to highlight the item and
then hit <enter>, or just type the capitalized letter
in the item you want.

~Creating Graphs

         Creating New Graphs

   You can create an new graph by selecting "New"
from the Main Menu.  This action will take you to
the New Graph menu, which looks like this:

Cycle
Difference
Empty
Group
K - complete
M - multipart
Petersen
Quadro
Random
S - Random tree
W - polycycle
coXeter
Y - Regular tree
Z - clone current

~Creating Graphs~Cycle

   A cycle is an n-gon.  EG prompts for n.

~Creating Graphs~Difference

   A difference graph is a superposition of n-stars. EG
will prompt for n and for a set of differences. For
example, the difference graph (7;1) is the septagon,
the difference graph (7;2) is a fat seven-pointed
star, the difference graph (7;3) is a sharp seven-
pointed star, and the difference graph (7;1,2) is
K7 less the sharp star.

~Creating Graphs~Empty

   An empty graph is a collection of disconnected
vertices; EG prompts for the number of vertices.

~Creating Graphs~Group

   Creates the Cayley graph of a group.  EG prompts
for the group, which it expects as a product of
cycles entered one at a time.   (?)

~Creating Graphs~K - Complete

   The complete graph on n vertices (denoted Kn,
e.g. K7) is an n vertex graph with all possible
edges.  EG prompts for n.

~Creating Graphs~Multipart

   The vertex set of a multipartite graph may be
partitioned into subsets such that every edge connects
vertices in different subsets.  EG creates complete
multipartite graphs and asks only for the number of
vertices in each part.  Thus, the number of parts is
specified implicitly.

~Creating Graphs~Petersen

   A generalized Petersen graph consists of an n-star
within an n-gon, connected by spokes.  More precisely,
a generalized Petersen graph contains an (n,1)
difference graph, an (n,k) difference graph, and a set
of "spokes" connecting vertices of the n-gon (the
(n,1) difference graph) with corresponding vertices of
the n-star (the (n,k) difference graph).  The usual
presentation of the Petersen graph is a generalized
Petersen graph with parameters 5 and 2.

   EG pops up a parameter entry box (q.v.) to obtain
the parameters n and k.

~Creating Graphs~Quadro

   This section not yet available.

~Creating Graphs~Random

   A random graph is defined by the number of vertices
in the graph and the probability of any particular edge
existing.  EG prompts for the number of vertices and
the edge probability.  An edge probability of 0 yields
an empty graph on n vertices; an edge probability of 1
yields the complete graph on n vertices.  Note that
there is nothing random about the number of vertices.

~Creating Graphs~S - Random Tree

   Creates a random tree according to some parameters
that I need to check.

~Creating Graphs~W - polycycle.

   A polycyclic graphs on parameters n and k consists
of k n-cycles with corresponding vertices joined.

~Creating Graphs~coXeter

   A generalized Coxeter graph consists of an n-star
within a n-star within an n-gon, connected by claws.
More precisely, a generalized Coxeter graph contains
an (n,1) difference graph, an (n,k) difference graph,
an (n,r) difference graph, and a set of "claws" (K1,3)
connecting vertices of the n-gon (the (n,1) difference
graph) with corresponding vertices of the stars.  The
usual presentation of the Coxeter graph is a generalized
Coxeter graph with parameters 7, 2, and 3.

   EG pops up a parameter entry box (q.v.) to obtain
the parameters n, k, and r.

~Creating Graphs~Y - Regular Tree

   A regular tree with parameters k and n is a tree
where all internal vertices (i.e. non-leaves) are of
degree k and n specifies which one.

~Creating Graphs~Z - clone current

   Creates a new copy of the graph currently selected
on the graph list.

~The graph list

   During an EG session, the program maintains a list of
available graphs.  Up to 6 of these graphs are displayed
at a time in a row at the bottom of the screen.  One of
the graphs in the list is called the "current graph"; it
is displayed in the third position from the left and is
highlighted.  The graph list may be rotated left or right,
graphs may be deleted or have their properties summarized,
and new graphs may be added either by creation within the
EG session or by importation from a file.

~The graph list~-> right and <- left

   The arrow keys rotate the graph list left and right.
The list is circular, that is, it has no end but wraps
back on itself.

~The graph list~Delete

   Delete removes the current graph from the graph list
and closes up the resulting hole in the list.  There is
no way to recover a deleted graph, so be careful.  If
the deletion results in an empty graph list some entries
on the main menu are greyed out.

~The graph list~Precis

  This section not yet available.

~Editing graphs

                 Editing Graphs

   This is the doorway to all the wonders of EG.  In
the hierarchy of command menus below Edit are
commands for:

  --  manipulating the structure of the graph

      --  altering vertices and edges
      --  coloring the graph
      --  constructing related graphs

  --  manipulating the picture of the graph

      --  tools for redrawing the graph
      --  tools for renaming vertices or graphs
      --  printing graphs

  --  analyzing the graph (calculating invariants)

~Editing graphs~Build graphs

   The Build graphs functions construct new graphs
from old ones.

~Editing graphs~Build graphs~Bipartite dbl

  This section not yet available.

~Editing graphs~Build graphs~Complement

   Creates the complement of the currently selected
graph.  The complement of a graph G is a graph whose
edges are all the non-edges of G.  For example, the
complement of a complete graph is an empty graph, and
vice versa.

~Editing graphs~Build graphs~pEndant

  This section not yet available.

~Editing graphs~Build graphs~F - pendant all

  This section not yet available.

~Editing graphs~Build graphs~dIstance

  This section not yet available.

~Editing graphs~Build graphs~J - polydist

  This section not yet available.

~Editing graphs~Build graphs~Line graph

  This section not yet available.

~Editing graphs~Build graphs~coNnected comp.

   Selects one or more connected components of the
currently selected graph.  EG prompts for a list of
vertices and then creates the graph that is the
subgraph of the currently selected graph induced by
the all the vertices in the connected components
containing the specified vertices.

~Editing graphs~Build graphs~pOwer

  This section not yet available.

~Editing graphs~Build graphs~Prism

  This section not yet available.

~Editing graphs~Build graphs~Two vanish

  This section not yet available.

~Editing graphs~Build graphs~fUse

  This section not yet available.

~Editing graphs~Build graphs~X - 2xedge

  This section not yet available.

~Editing graphs~Build graphs~Y - 3xedge

  This section not yet available.

~Editing graphs~Build graphs~Z - neighbor

  This section not yet available.

~Editing graphs~Color edges

  This section not yet available.

~Editing graphs~Color edges~Cycle

  This section not yet available.

~Editing graphs~Color edges~Incident

  This section not yet available.

~Editing graphs~Color edges~Matching

  This section not yet available.

~Editing graphs~Color edges~iNduced

  This section not yet available.

~Editing graphs~Color edges~Path

  This section not yet available.

~Editing graphs~Color edges~Reset

  This section not yet available.

~Editing graphs~Color edges~Shift

  This section not yet available.

~Editing graphs~Color edges~Total

  This section not yet available.

~Editing graphs~Color edges~What color

  This section not yet available.

~Editing graphs~Draw

   The representation or visual presentation of a graph
is distinct from its structure:  there may be several
different interesting drawings of a single graph.  (See,
for example, the drawings of the Petersen graph in the
EG manual.)

   The functions on the Draw menu change the displayed
drawing of the currently selected graph, but do not
chnange its structure.

~Editing graphs~Draw~Bipartition

  This section not yet available.

~Editing graphs~Draw~Clean

   Clean implements an algorithm due to Nate Dean
(of AT&T Bell Labs).  EG prompts for a list of vertices
to "still", places those vertices equally spaced around
a circle in the specified order with the first vertex
in the list at 3 o'clock, and then places the other
vertices of the graph in the interior of the circle
according to an averaging algorithm.

   Clean does not work well on graphs with vertices of
degree 1.

~Editing graphs~Draw~Findcycle

  This section not yet available.

~Editing graphs~Draw~Hamilton

  This section not yet available.

~Editing graphs~Draw~dIstance

  This section not yet available.

~Editing graphs~Draw~Mouse

   Activates the mouse for moving vertices.  Click the
left button on the vertex you wish to move, move the
outline to the desired new location of the vertex, and
then click the laft button again to place the vertex.

~Editing graphs~Draw~Normalize

   Resizes the graph to fill a standard bounding box.
This function is useful is other drawing functions (such
as Springs) have shrunk the graph to a uselessly small
size.

~Editing graphs~Draw~Parameters

  This section not yet available.

~Editing graphs~Draw~Rotate

   EG prompts for a number of degrees and then rotates
the graph that many degrees widdershins.

   Hint:  if I'd meant clockwise, I would have said
clockwise.

~Editing graphs~Draw~Springs

  This section not yet available.

~Editing graphs~Draw~Tiny

  This section not yet available.

~Editing graphs~Draw~U - mouse repos

   This function allows the user to resize and reposition
the currently selected graph.

~Editing graphs~Draw~Warp

  This section not yet available.

~Editing graphs~Draw~Y - strain

  This section not yet available.

~Editing graphs~Draw~Z - strain tol

  This section not yet available.

~Editing graphs~toggle Edges

   These functions add and remove edges from the
currently selected graph.

   In many cases, EG adds and removes edges
symmetrically:  the user gives a specification and
then EG removes the specified edges if they are
present or adds them if they are absent.  Hence
the description "toggle".

~Editing graphs~toggle Edges~By color

  This section not yet available.

~Editing graphs~toggle Edges~Cycle

  This section not yet available.

~Editing graphs~toggle Edges~Edge color

  This section not yet available.

~Editing graphs~toggle Edges~Matching

   Since vertices have names but edges do not, an edge
is specified in EG by the pair of vertices it connects.
A matching is a list of one or more pairs of vertices.
EG is quite flexible about delimiters:  you may use
spaces or commas between the elements of a pair and
between pairs.

~Editing graphs~toggle Edges~Path

  This section not yet available.

~Editing graphs~toggle Edges~Star

  This section not yet available.

~Editing graphs~F - color vertices

  This section not yet available.

~Editing graphs~F - color vertices~Bicolor

  This section not yet available.

~Editing graphs~F - color vertices~Components

  This section not yet available.

~Editing graphs~F - color vertices~Eccentricity

  This section not yet available.

~Editing graphs~F - color vertices~by deGree

  This section not yet available.

~Editing graphs~F - color vertices~by dIstance

  This section not yet available.

~Editing graphs~F - color vertices~Mouse

  This section not yet available.

~Editing graphs~F - color vertices~Name

  This section not yet available.

~Editing graphs~F - color vertices~Proper

  This section not yet available.

~Editing graphs~F - color vertices~Reset

  This section not yet available.

~Editing graphs~F - color vertices~Shift

  This section not yet available.

~Editing graphs~F - color vertices~What color

  This section not yet available.

~Editing graphs~Invariants

   An invariant of a graph is a property of the graph
that has the same value for all graphs isomorphic to
the original graph.  (Hence the name:  it doesn't vary.)
Invariants are extremely useful in studying isomorphism,
as two graphs with different values of an invariant
are not isomorphic.  (Beware the converse!)  A
considerable amount of effort has also been directed
towards the study of certain classes of graphs (where
a class is characterized by having the same value of
some invariant.)

~Editing graphs~Invariants~diAmeter

  This section not yet available.

~Editing graphs~Invariants~Cycle

  This section not yet available.

~Editing graphs~Invariants~Eccentricity

  This section not yet available.

~Editing graphs~Invariants~deGrees

   Reports the degree sequence of the graph.   The
degree sequence is returned as a series of terms of
the form d^r, where d is a degree that occurs in the
graph and r is the number of vertices of that degree.
The series is sorted in increasing order of degree.
For example, the degree sequence 1^2 2^3 3^4 indicates
that the graph has two vertices of degree one, three
vertices of degree two, and four vertices of degree
three.

   Note that this function implicitly returns both the
min-degree and the max-degree of the graph:  just look
at the first and last degree values in the sequence.

   A k-regular graph on n vertices has a degree sequence
with exactly one term, k^n.

~Editing graphs~Invariants~gIrth

  This section not yet available.

~Editing graphs~Invariants~K - clique finder

  This section not yet available.

~Editing graphs~Invariants~coNnected comp.

   Returns the number of connected components of
the currently selected graph.

   A graph with one connected component is called
connected.

~Editing graphs~Invariants~Precis

  This section not yet available.

~Editing graphs~Invariants~Q - edges

   Returns the number of edges in the currently
selected graph.

~Editing graphs~Invariants~Radius

  This section not yet available.

~Editing graphs~Invariants~diStances

  This section not yet available.

~Editing graphs~Invariants~dist sUbmat

  This section not yet available.

~Editing graphs~Invariants~Vertices

   Returns the number of vertices in the currently
selected graph.

~Editing graphs~Kill vertices

   The functions in the Kill vertices menu remove
one or more vertices and all edges incident upon
those vertices from the current graph.

~Editing graphs~Kill vertices~by Anticolor

  This section not yet available.

~Editing graphs~Kill vertices~By name

   EG prompts for a list of vertices to remove and
then removes them.  Technically, if X is the set of
vertices entered then the result is the subgraph
induced by V(G) - X.

~Editing graphs~Kill vertices~by Color

  This section not yet available.

~Editing graphs~Kill vertices~by deGree

  This section not yet available.

~Editing graphs~Names

   Each graph in the graph list has a name, twelve
characters of which fit above the graph in the
graph list without interfering with the names of
other graphs.

   Each vertex in a graph has a name.  Vertex names
generally start out as 0,1,2,3,..., but a number of
graph operations (e.g., line graph) build graphs with
names that give information about their origin.

~Editing graphs~Names~Graph name

   Changes the name of the currently selected graph.

~Editing graphs~Names~Reset names

  This section not yet available.

~Editing graphs~Postscript

  This section not yet available.

~Editing graphs~Postscript~Edge

  This section not yet available.

~Editing graphs~Postscript~HPL dump

  This section not yet available.

~Editing graphs~Postscript~Plain

  This section not yet available.

~Editing graphs~Postscript~Set gray

  This section not yet available.

~Editing graphs~Save and Quit

   Quit closes the editing session *without* updating
the graph on the graph list.  Thus, if you have put
some effort into creating a graph and then accidentally
kill all the vertices, you have some hope of recovery.
Save, on the other hand, preserves your changes
in the graph list.   (Which may be just what you want.)

~Editing graphs~add Vertices

   The options on the Add vertices menu allow you to
add new elements to the vertex set of the currently
selected graph.  These new elements can be entirely
disconnected, connected to each other in certain ways,
or connected (in certain ways) to vertices already in
the graph.

~Editing graphs~add Vertices~Add vertices

   Adds one or more disconnected vertices.  EG prompts
for the number of vertices to add and then puts that
many vertices into the currently selected graph.

~Editing graphs~add Vertices~insert by Color

  This section not yet available.

~Editing graphs~add Vertices~Duplicate

  This section not yet available.

~Editing graphs~add Vertices~Insert vert

  This section not yet available.

~Editing graphs~add Vertices~J - insert all

  This section not yet available.

~Editing graphs~add Vertices~K - insert wedge

  This section not yet available.

~Editing graphs~add Vertices~Mouse add

   Activates the mouse for adding new vertices.  Move
the mouse to the place where you want a new vertex and
click the left button to place the vertex.  Repeat until
you have added all the vertices you wany, then click on
the word "DONE" in the upper left corner of the graph
window.

~Editing graphs~add Vertices~Selected

  This section not yet available.

~Graph Files

                 EG and disk files

   EG stores graph information on disk in a format
called a Graph Description File.  The .GDF format is
documented in an appendix to the EG manual.  The
format is not too obscure, however, and it should not
be too difficult for anyone with some programming
experience to write code that will translate your
favorite graph file format into .GDF format.

   Since .GDF files are ASCII, they can be read using
your favorite text editor.  The adventurous are
encouraged to reverse engineer the format.

   If you use EG to read and write files, you don't
need to worry about the .GDF format at all:  EG will
take care of all the details.

   EG is also able to import and export graphs in a
number of other formats; this functionality is provided
to make it easier to move graphs between EG and other
software.

~Graph Files~Read

                 Reading Files

   EG stores graphs in a format called a Graph
Description File.

   "Read" will prompt for a file name.  You may specify
either a file name, e.g. SAMPLES.GDF, which will be
assumed to reside in the current directory, or a
complete path, e.g. C:\GRAPH\EG\MYGRAPHS.GDF.  If you
do not specify a file extension, EG will assume that
the file extension is supposed to be .GDF.

   Once it finds the .GDF file, EG will read in all
the graphs in the file and add them onto the Graph
Stack.  There is no way to load graphs selectively:
if you want just one graph from a file, you must load
all the graphs in that file and then delete the ones
you don't want.

~Graph Files~Write

                 Writing Files

   "Write" will prompt for a file name and will then
save the entire Graph Stack to that file, using .GDF
format.

  It is possible to save structure information
about a graph in other formats:  read the entries
explaining the Files menu.

   As with reading a file, you can specify a file name
in the current directory or a path.  If the file you
specify already exists, EG will DO SOMETHING.

   If you do not specify an extension, EG will supply
the extension .GDF for you.

~Graph Files~Files

  This section not yet available.

~Graph Files~Files~Adjacency exp

  This section not yet available.

~Graph Files~Files~Chroma exp

  This section not yet available.

~Graph Files~Files~Distance exp

  This section not yet available.

~Graph Files~Files~GAP mat exp

  This section not yet available.

~Graph Files~Files~cHord imp

  This section not yet available.

~Graph Files~Files~import Adj

  This section not yet available.

~Graph Files~Files~J - import nbr

  This section not yet available.

~Graph Files~Files~Neighbor exp

  This section not yet available.

~Graph Files~Files~Read

  This section not yet available.

~Graph Files~Files~Write

  This section not yet available.

~Miscellany

   This section not yet available.

~Miscellany~Seed

  This section not yet available.

~Miscellany~Z - special

  This section not yet available.

~Getting OUT

                 Getting OUT

   The control menus for EG are structured like a
tree, and the command required to return to the
previous level of the tree (or, if you are at the Main
Menu, to leave EG entirely) depends on where you are
in the tree.

   At the Main Menu, hit X to exit EG.  If you have
created graphs that have not been saved to the disk,
EG will ask you to confirm that you really want to
quit without saving.


   At other menus, either Q (for Quit) or D (for
Done) will close the menu and return you to the
next level up.  There is one important variation:
you can exit the Edit menu by typing either Q or
S (for Save).  The difference is that Q closes the
editing session *without* updating the graph on the
graph list.  Thus, if you have put some effort into
creating a graph and then accidentally kill all
the vertices, you have some hope of recovery.
Save, on the other hand, preserves your changes
in the graph list.

   A suggested way to use EG to create a complex
graph (or to search for a graph with particular
properties) is to choose some starting point, edit
for a while, save your work to the graph list when
you think that you have made some progress, and then
use New/Z - clone current to make a new copy on which
to continue working.

   Comments, error messages, and informational messages
are removed from the screen by any keystroke.  These
popup windows are generally accompanied by the "Hit
any key to continue" reminder.

~Disclaimer
   This software was written by Dan Ashlock.  The help
files and documentation were written by David Schweizer.
Both of us tried not to make mistakes but do not have
sufficient taxpayer supplied grant money for there to
be any hope there are not dozens of mistakes (funding
to date, about $0.69).  Because of this we make no
promises whatsoever for the suitability of this software
for any particular use.  We assume no responsibility for
those of you that figure out how to reformat the CD-roms
on the network server at your place of work using this
software.  We disclaim any responsibility for anything
bad that happens to you if you use this software.  You
would have to be a complete fool to even touch this
software.  This software may cause cancer in lab rats.
Pregnant rats should not use this software but may read
the documentation.  EG3 copyright 1996 by Dan Ashlock.
EG3 help and documentation copyright 1996 by David
Schweizer.

~EOF