Answered: Explain how a directed graph's vertex…

Explain how a directed graph's vertex u, which includes both incoming and outgoing edges in G, may end up in a depth-first tree that only contains u.

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Concept explainers

Depth First Search

Depth-first search (DFS) also known as Depth First traversal is an algorithm used to traverse or search the nodes in a tree or graph data structure. Traversal usually means visiting all the nodes of a graph. DFS performs in a depth-ward manner. It uses a stack to remember the vertices it has visited. The search starts from the root node, where any arbitrary node is selected as a root node in a graph, and then each node is explored along each branch before performing backtracking. The DFS algorithm uses a recursive technique by following the idea of backtracking. DFS algorithm does this by performing an in-depth search of all the nodes by traversing in a forward direction. If the required node is not found, it starts backtracking to previously visited nodes.

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Explain how a directed graph's vertex u, which includes both incoming and outgoing edges in G, may end up in a depth-first tree that only contains u.

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Step 1: Introduction

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Step 2: Depth-First Search and Directed Graphs

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Step 3: DFS Algorithm and Vertex Isolation

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Step 4: Graph Structure and Vertex Isolation

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