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Extensive-form games can be described by a "game tree," in which each turn is a vertex of the tree, with each branch indicating the players' successive choices.
Let be a vertex of the tree.
Let W be a vertex of Γ.
Otherwise, always falls on a vertex of.
(i) Let W be a vertex of Γ.
Then this is achieved when touches a vertex of.
A pendent vertex is a vertex of degree one.
(ii) Otherwise, always falls on a vertex of. .
(iii) If, or, is achieved on a vertex of if.
A vertex of degree 1 is said to be a pendent vertex, while a vertex of degree at least 2 is said to be a non-pendent vertex.
If an edge connects a vertex of degree i and a vertex of degree j in G, then we call it an ((i,j -edge.
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