Definition: A rooted m-ary tree of height h is balanced if all leaves are.

\begingroup I think all it takes is for that edge to exist. In your example, remove an edge other than the middle one and you get one tree having 3 vertices. \endgroup – Manuel Lafond Feb 11 '15 at Question: Question 3 If we remove an abitrary edge from a tree, then the resulting graph will be Not yet answered Points out of Select one: O a.

Using the following remarkable theorem of Aldous and Broder: Start at an arbitrary vertex s and take a random walk until every vertex has been visited choosing an outgoing edge uniformly at random among all incident edges.

a connected graph O b. a cyclic graph Flag question O c. two disjoint trees O d. several trees O e. a tree Clear my choice Question 4 If we remove an edge from an m-ary tree (keeping the same set. Remove an edge from a tree and it becomes disconnected. Add an edge to a tree and it introduces a cycle. An m-ary tree is a rooted tree in which each vertex has at most m children.

The key is to note that our only interest is in the minimal edge from each non-tree vertex to a tree vertex.

In CSE we saw 2-ary (or binary) trees. We also tend in computer science to deal with what are called ordered trees, where the order of the children matters. A tree by definition is a graph having N vertices and N-1 edges in such a way that each vertex has at least one edge. Simple intuition will show you that the Nth edge will create a cycle (small or big depending on the connectivity).

Once you have Missing: m-ary tree. It can be proved by showing proof to any of the properties of tree. A graph having no cycles is said to be acyclic. A forest is an acyclic graph. A tree is a connected graph without any cycles, or a tree is a connected acyclic graph.

The edges of. Def An m-ary tree (m 2) is a rooted tree in which every vertex has m or fewer children. Def A complete m-ary tree is an m-ary tree in which every internal vertex has exactly m children and all leaves have the same depth. Example Fig shows two ternary (3-ary) trees; the one on the left is complete; the other one is not.

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