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Math 61 Post-Midterm 2

Terms in this set (16)

matching
subset M of E of edges such that no two edges in M are incident on the same vertices. Matching covers set S of vertices if every vertex in S is incident to some edge in M
tree
graph such that for every u,v of vertices in V, there is exactly one simple path from u to v
rooted tree
tree where one vertex is designated as the root
acyclic
graph has no cycles
spanning tree
T, a tree in G, such that T has every vertex in G. T must use at least one edge from every cutset
minimal spanning tree
T, a spanning tree in G, such that the total weight is as small as possible. Can find using Prim's Algorithm
cut
in a graph is a partition of V into two sets
associated cutset
set of edges incident to vertex in R and vertex in S of cut
height of rooted tree
largest n such that there is some vertex at level n
level of a tree
1 more than the number of edges between given nodes and the root
child of vertex
if vertex is at level n, children are neighbors at level n+1
terminal vertex/leaf
vertex with no children
internal vertex
nonterminal vertex
binary tree
rooted tree where every vertex has either 0, 1, or 2 children
complete binary tree
binary tree of height h such that every vertex at level n for n<h has two children.
has 2^n vertices at each level.
has 2^h total leaves.
has 2^h-1 total internal vertices
full binary tree
binary tree where every vertex has either 0 or 2 children
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