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**PROGRAM:**

**NAME**

gvgen - generate graphs

**SYNOPSIS**

**gvgen**[

**-dv?**] [

**-i**

__n__] [

**-c**

__n__] [

**-C**

__x,y__] [

**-g**

__[__

**f**

__]x,y__] [

**-G**

__[__

**f**

__]x,y__] [

**-h**

__n__] [

**-k**

__n__] [

**-b**

__x,y__] [

**-B**

__x,y__] [

**-m**

__n__] [

**-M**

__x,y__] [

**-p**

__n__] [

**-r**

__x,y__] [

**-R**

__x__] [

**-s**

__n__] [

**-S**

__n__] [

**-t**

__n__] [

**-t**

__d,n__] [

**-T**

__x,y__] [

**-T**

__x,y,u,v__] [

**-w**

__n__] [

**-n**

__prefix__] [

**-N**

__name__] [

**-o**

__outfile__]

**DESCRIPTION**

**gvgen**generates a variety of simple, regularly-structured abstract graphs.

**OPTIONS**

The following options are supported:

**-c**

__n__Generate a cycle with

__n__vertices and edges.

**-C**

__x,y__Generate an

__x__by

__y__cylinder. This will have

__x*y__vertices and

__2*x*y__

__-__

__y__edges.

**-g**

__[__

**f**

__]x,y__

Generate an

__x__by

__y__grid. If

**f**is given, the grid is folded, with an edge attaching

each pair of opposing corner vertices. This will have

__x*y__vertices and

__2*x*y__

__-__

__y__

__-__

__x__edges if unfolded and

__2*x*y__

__-__

__y__

__-__

__x__

__+__

__2__edges if folded.

**-G**

__[__

**f**

__]x,y__

Generate an

__x__by

__y__partial grid. If

**f**is given, the grid is folded, with an edge

attaching each pair of opposing corner vertices. This will have

__x*y__vertices.

**-h**

__n__Generate a hypercube of degree

__n__. This will have

__2^n__vertices and

__n*2^(n-1)__edges.

**-k**

__n__Generate a complete graph on

__n__vertices with

__n*(n-1)/2__edges.

**-b**

__x,y__Generate a complete

__x__by

__y__bipartite graph. This will have

__x+y__vertices and

__x*y__

edges.

**-B**

__x,y__Generate an

__x__by

__y__ball, i.e., an

__x__by

__y__cylinder with two "cap" nodes closing the

ends. This will have

__x*y__

__+__

__2__vertices and

__2*x*y__

__+__

__y__edges.

**-m**

__n__Generate a triangular mesh with

__n__vertices on a side. This will have

__(n+1)*n/2__

vertices and

__3*(n-1)*n/2__edges.

**-M**

__x,y__Generate an x by y Moebius strip. This will have

__x*y__vertices and

__2*x*y__

__-__

__y__edges.

**-p**

__n__Generate a path on

__n__vertices. This will have

__n-1__edges.

**-r**

__x,y__Generate a random graph. The number of vertices will be the largest value of the

form

__2^n-1__less than or equal to

__x__. Larger values of

__y__increase the density of the

graph.

**-R**

__x__Generate a random rooted tree on

__x__vertices.

**-s**

__n__Generate a star on

__n__vertices. This will have

__n-1__edges.

**-S**

__n__Generate a Sierpinski graph of order

__n__. This will have

__3*(3^(n-1)__

__-__

__1)/2__vertices

and

__3^n__edges.

**-t**

__n__Generate a binary tree of height

__n__. This will have

__2^n-1__vertices and

__2^n-2__edges.

**-t**

__h,n__Generate a n-ary tree of height

__h__.

**-T**

__x,y__

**-T**

__x,y,u,v__

Generate an

__x__by

__y__torus. This will have

__x*y__vertices and

__2*x*y__edges. If

__u__and

__v__

are given, they specify twists of that amount in the horizontal and vertical

directions, respectively.

**-w**

__n__Generate a path on

__n__vertices. This will have

__n-1__edges.

**-i**

__n__Generate

__n__graphs of the requested type. At present, only available if the

**-R**flag

is used.

**-n**

__prefix__

Normally, integers are used as node names. If

__prefix__is specified, this will be

prepended to the integer to create the name.

**-N**

__name__

Use

__name__as the name of the graph. By default, the graph is anonymous.

**-o**

__outfile__

If specified, the generated graph is written into the file

__outfile.__Otherwise, the

graph is written to standard out.

**-d**Make the generated graph directed.

**-v**Verbose output.

**-?**Print usage information.

**EXIT** **STATUS**

**gvgen**exits with 0 on successful completion, and exits with 1 if given an ill-formed or

incorrect flag, or if the specified output file could not be opened.

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