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Tree Graphs

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has exactly one more vertex than it has edges.

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Magic Caterpillars

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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Plum Tree

Label this plum tree graph to make it totally magic!

Magic W

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
Even though this subject is accessible to school students, Magic Graphs is currently an active research field (see Joseph Gallian's website http://citeseer.ist.psu.edu/gallian00dynamic.html which lists all the papers published on the subject).