Modern Math Spanning Trees

Front

What is a cycle in graph theory?

Back

A path that starts and ends at the same vertex and does not use any edge more than once.

Front

What is a Spanning Tree?

Back

A subgraph that includes all the vertices of the original graph and is a tree (connected and acyclic).

Front

What is a Minimum Spanning Tree?

Back

A spanning tree with the minimum possible total edge weight.

Front

How do you determine the number of spanning trees in a graph?

Back

Using Kirchhoff's matrix tree theorem or by counting the spanning trees directly.

Front

What does it mean for a graph to be acyclic?

Back

It means the graph does not contain any cycles.

Front

What is a subgraph?

Back

A graph formed from a subset of the vertices and edges of another graph.

Front

What is the difference between a tree and a spanning tree?

Back

A tree is a connected acyclic graph, while a spanning tree includes all vertices of a graph.

Front

Can a graph have more than one spanning tree?

Back

Yes, a graph can have multiple spanning trees.

Front

What is the significance of spanning trees in network design?

Back

They ensure all nodes are connected with the minimum number of edges.

Front

What is the relationship between spanning trees and cycles?

Back

A spanning tree cannot contain any cycles.