What is a cycle graph $$C_n$$ ?

A cycle graph $$C_n$$ is a graph that consists of a single cycle, where each of the $$n$$ vertices is connected in a closed loop. Each vertex has degree 2.

How many edges does a complete graph $$K_n$$ have?

A complete graph $$K_n$$ has $$\frac{n(n-1)}{2}$$ edges.

How many edges are there in a complete graph $$K_5$$ ?

There are 10 edges in a complete graph $$K_5$$ .

What is the formula for the degree of a vertex in a cycle graph $$C_n$$ ?

In a cycle graph $$C_n$$ , the degree of each vertex is 2.

What is the significance of the order of a graph?

The order of a graph is the number of vertices in the graph.

What does it mean for a graph to be connected?

A graph is connected if there is a path between every pair of vertices.

What is an edge in graph theory?

An edge is a connection between two vertices in a graph.

What is the difference between a path and a cycle in graph theory?

A path does not revisit any vertex, while a cycle starts and ends at the same vertex.

How do you determine if a sequence of vertices forms a path in a graph?

A sequence of vertices forms a path if each consecutive pair of vertices is connected by an edge.

What is the maximum degree of a vertex in a complete graph $$K_n$$ ?

The maximum degree of a vertex in a complete graph $$K_n$$ is $$n-1$$ .

What is the relationship between the number of vertices and edges in a complete graph?

In a complete graph $$K_n$$ , the number of edges is given by the formula $$\frac{n(n-1)}{2}$$ , which grows quadratically with the number of vertices.

Exploring Graph Theory Concepts Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

2.

FLASHCARD QUESTION

Front

What is the degree of each vertex in a complete graph with order 5?

Back

In a complete graph with order 5, each vertex has a degree of 4.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What is a path in graph theory?

Back

A path is a sequence of edges that connects a sequence of vertices without revisiting any vertex.

6.

FLASHCARD QUESTION

Front

What is the definition of a complete graph?

Back

A complete graph is a graph in which every pair of distinct vertices is connected by a unique edge.

7.

FLASHCARD QUESTION

Front

What is the degree of a vertex in a graph?

Back

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

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