magic pentagram | magic star

An edge-magic graph is a labeled graph with e graph edges labeled with distinct elements {1, 2, ..., e} so that the sum of the graph edge labels at each graph vertex is the same. A vertex-magic graph labeled graph vertices which give the same sum along every straight line segment. No magic pentagrams can be formed with the number 1, 2, ..., 10 (Trigg 1960; Langman 1962, pp. 80-83; Dongre 1971; Richards 1975-1978; Trigg 1998), but 168 almost magic pentagrams (in which the sums are the same for four of the five lines) can. The figure above show a magic pentagram with sums 24 built using the labels 1, 2, 3, 4, 5, 6, 8, 9, 10, and 12.

antimagic graph | labeled graph | magic circles | magic constant | magic cube | magic hexagon | magic square