Drawing tool for graphs (town-road maps); also contains a few associated brain teasers.

In mathematics a 'graph' is like a map of towns connected by roads.
The towns are called vertices or nodes and the connecting roads are called edges.
Note that a bend in a polyline is NOT a vertex unless marked as such.

Menu options:
Usually you will only use the options POLYLINE, DEGREES, CORNERS, COUNT V and COUNT F.

BRUSH: The option BRUSH lets you select an icon and place it onto a single position of the board. For straight pieces, the system will (try to) insert lines without deleting existing ones. Boxed icons are for vertices. Some contain numbers, usually used to show the 'degree' of a vertex (i.e., how many lines converge at this vertex, or how many roads meet at this town).
Unboxed numbers can be used to mark an area, showing the number of vertices (roads) around an area.
Click a token from the list at any time; the sytem will automatically invoke BRUSH mode!
RND DROP: drops a selected item onto a random empty position with no neighbours.
DELETE: click a position to delete its content.
DEL EDGE: Deletes a clicked polyline. Also deletes a clicked vertex.
DEL VERT: Deletes all polylines connected to a vertex. Also deletes a clicked polyline.
RED/BLACK: change ink for (poly)lines. (Note that crossing lines can only be either red or black!).
LINE: The LINE option lets you draw long straight lines. A straight line cannot cross a bend.
POLYLINE: When using POLYLINE, remember that you have to finish the polyline before you can start another polyline.
To finish a polyline, click the end piece again or select any drawing mode from the list.
OVERWRITE: click here to stop the POLYLINE and LINE options from overwriting the boxed numbers.
POLYTRACE: Retrace a path of consecutive nodes and polylines, starting and ending at a node while painting the path red in the process. Useful to find loops etc; see variant 'Hamilton Puzzle'.
DEGREES: Calculates the number of roads converging at each town (the 'degree' of each vertex). The degree will appear as a digit inside the vertex box.
VERIFY V: checks that the boxed numbers correspond with the edges converging at the vertex.
CORNERS: An area surrounded by roads is called a 'face'. Hit the CORNERS button, then click a face to have the system count the vertices or lines (towns or roads) around a face.
Note that bends in the path do NOT count as vertices of graphs.
The number of vertices will be displayed at the empty position you clicked.
This feature only works if the area you clicked has no crossing path pieces at its boundary.
COUNT V: Hit the COUNT V button to count the vertices (towns) on the board.
COUNT F: Hit the COUNT F button to count the areas (faces) on the board. (To be precise: COUNT F counts the connected sets of empty positions).
AREAS: Similar to COUNT F, in addition each area (face) is marked by an 'A' on yellow background.
Warning: Areas which do not contain at least one empty board position will not be marked or counted. Click the 'areas' button again to delete all 'A' markings.

Default variant : Freeplay - create your own graphs
Puzzle variants: Several variants are attached which contain special graph puzzles you have to solve. Please read the associated game text for details.

Note: Do not place two towns (vertices) next to each other, neither orthogonally nor diagonally.
Also, areas which do not contain at least one empty board position will not be marked or counted.

Please note that there are several alternative piece sets available, including a black-and-white one.

More exmaples of alternating planar graphs can be found here: http://demonstrations.wolfram.com/AlternatingPlanarGraphs/

Related Zillions games: Roadmaps, Draw, Isolattice, Lattice, Linedraw.

Warning: In graphs with more than 40 vertices clicking option 'COUNT FACES' can lead to the Zillions error message 'Infinite Loop Detected' after which Zillions shuts down. This is not caused by a programming error in the zrf, but by a Zillions limitation.

If not mentioned otherwise (see associated game texts), all solutions are by the author.