Proof of a Tree's Edges with Basis and Inductive Steps
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Questions and Answers

a tree with n vertices has n-1 edges prove it with basis steps and inductive step

What is the purpose of topological sort?

To obtain a linear ordering of the vertices in a directed graph or tree.

Name three applications of trees in computer science.

Data structures, algorithms, and computer graphics.

What is a binary tree and how many children can a node have?

<p>A binary tree is a tree where each node has at most two children.</p> Signup and view all the answers

What type of trees are used in database management systems and file systems?

<p>Binary search trees.</p> Signup and view all the answers

How do binary trees contribute to computer vision?

<p>They are used for image processing and feature extraction.</p> Signup and view all the answers

What is a tree in the context of discrete mathematics?

<p>An undirected graph that is connected and acyclic, with a root vertex and internal vertices.</p> Signup and view all the answers

What are the main traversal techniques for trees?

<p>Depth-First Search (DFS) and Breadth-First Search (BFS).</p> Signup and view all the answers

What is the root-to-leaf path in a tree?

<p>The edge connecting a vertex to its parent.</p> Signup and view all the answers

What is the depth of a tree?

<p>The sum of the lengths of the root-to-leaf paths.</p> Signup and view all the answers

What are the types of vertices in a tree?

<p>Root, internal, and leaves.</p> Signup and view all the answers

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