Flashcard on Vertex Degrees

Front

What is a Hamilton Circuit?

Back

A Hamilton Circuit is a path in a graph that visits each vertex exactly once and returns to the starting vertex.

Front

What is Kruskal's Algorithm used for?

Back

Kruskal's Algorithm is used to find the minimum spanning tree of a graph by adding edges in increasing order of weight without forming cycles.

Front

What does the degree of a vertex represent?

Back

The degree of a vertex is the number of edges connected to it.

Front

How do you determine if a path is a Hamilton Circuit?

Back

A path is a Hamilton Circuit if it visits every vertex exactly once and returns to the starting vertex.

Front

What is the significance of a minimum cost spanning tree?

Back

A minimum cost spanning tree connects all vertices in a graph with the least total edge weight.

Front

Can a graph have more than one Hamilton Circuit?

Back

Yes, a graph can have multiple Hamilton Circuits depending on its structure.

Front

What is the difference between a Hamilton Circuit and a Hamilton Path?

Back

A Hamilton Circuit returns to the starting vertex, while a Hamilton Path does not.

Front

What is a spanning tree?

Back

A spanning tree is a subgraph that includes all vertices and is a tree (no cycles) with the minimum number of edges.

Front

What does it mean if the degree of a vertex is 0?

Back

If the degree of a vertex is 0, it means that the vertex is isolated and has no edges connected to it.

Front

What is the purpose of graph representation in maps?

Back

Graph representation in maps helps visualize relationships and connections between different regions.