Question

Which of the graphs are trees? Explain.

   Which of the graphs are trees? Explain.

Discrete Mathematics

Discrete Mathematics

Richard Johnsonbaugh 8th Edition

Chapter 9, Problem 1

Instant Answer

Solved by Expert Chris Trentman

03/13/2021

Step 1

This means that there is exactly one path between any two vertices, and there are no cycles (closed loops) in the graph. Show more…

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Which of the graphs are trees? Explain.

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Key Concepts

Tree

A tree is a type of graph that is both connected and acyclic. This means that for a graph to be considered a tree, there must be a path between every pair of vertices, and it must contain no cycles. Additionally, a tree with n vertices always has exactly n-1 edges.

Graph Connectivity

Graph connectivity refers to the property of a graph wherein there is a route between every pair of vertices. This is an essential criterion for trees because if a graph is not fully connected, it cannot be classified as a tree.

Acyclic Graph

An acyclic graph is one that does not contain any cycles, which means there are no paths that start and end at the same vertex while traversing other vertices. This characteristic is a key requirement for a graph to be considered a tree.

Cycle

A cycle in a graph is a path that begins and ends at the same vertex without repeating any edges or vertices (except the ones at the start and end). Identifying cycles is crucial when determining whether a graph qualifies as a tree, as any cycle disqualifies the graph from being a tree.

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