Magic Graph

A Labeled Graph with $e$ Edges labeled with distinct elements $\{1, 2, \ldots, e\}$ so that the sum of the Edge labels at each Vertex is the same. Another type of magic graph, such as the Pentagram shown above, has labeled Vertices which give the same sum along every straight line segment (Madachy 1979).

See also Antimagic Graph, Labeled Graph, Magic Circles, Magic Constant, Magic Cube, Magic Hexagon, Magic Square

References

Hartsfield, N. and Ringel, G. Pearls in Graph Theory: A Comprehensive Introduction. San Diego, CA: Academic Press, 1990.

Heinz, H. ``Magic Stars.'' http://www.geocities.com/CapeCanaveral/Launchpad/4057/magicstar.htm.

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 98-99, 1979.