Advanced Graph Terminology and Structural Concepts Quiz

1) A graph consists of:

Vertices only

Edges only

Vertices and edges

Paths only

A graph is defined by its vertex set and edge set.

Explanation

A graph is defined by its vertex set and edge set.

Advanced Graph Terminology and Structural Concepts Quiz - Quiz

Think you’re comfortable with basic graph vocabulary? This quiz takes you into deeper territory, where you’ll apply core definitions to more sophisticated structures like cycle graphs, bipartite graphs, degree sequences, and the behavior of loops and parallel edges. You’ll analyze how degrees are counted, interpret structural properties of trees, and... see morereason about connectivity, complexity, and graph realizability. Through a combination of conceptual questions and short problem-solving tasks, you’ll see how precise terminology helps uncover powerful patterns within networks and mathematical structures. By the end, you’ll have a sharper, more rigorous understanding of how graph theory describes complex systems.
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2) Two vertices connected by an edge are called:

Adjacent

Parallel

Independent

Weighted

Adjacent means joined by an edge.

Explanation

Adjacent means joined by an edge.

3) In an undirected graph, edges have no orientation.

True

False

Undirected edges do not point from one vertex to another.

Explanation

Undirected edges do not point from one vertex to another.

Submit

5) Which graph cannot be bipartite?

A tree

A cycle of even length

A cycle of odd length

A graph with only two vertices

Odd cycles are not bipartite.

Explanation

Odd cycles are not bipartite.

6) The degree of a vertex is:

The number of loops in the graph

The number of edges touching the vertex

The number of vertices in the graph

The number of paths starting at the vertex

Degree counts incident edges.

Explanation

Degree counts incident edges.

7) A loop contributes how much to the degree of a vertex?

Depends on the graph

A loop touches the vertex twice.

Explanation

A loop touches the vertex twice.

8) A simple graph has no loops and no multiple edges.

True

False

Simplicity prohibits both loops and parallel edges.

Explanation

Simplicity prohibits both loops and parallel edges.

9) A connected graph must contain at least one cycle.

True

False

Trees are connected and acyclic.

Explanation

Trees are connected and acyclic.

10) A simple graph has 5 vertices and 6 edges. Which must be true?

It is a tree

It is disconnected

At least one vertex has degree ≥ 3

All degrees must be even

Total degree=12 ⇒ avg=2.4 ⇒ some ≥3.

Explanation

Total degree=12 ⇒ avg=2.4 ⇒ some ≥3.

11) Which of the following are examples of simple graphs?

A triangle (3-cycle)

A single vertex with a loop

A graph with two vertices and one edge between them

A graph with two parallel edges

Loops and parallel edges are not allowed in simple graphs.

Explanation

Loops and parallel edges are not allowed in simple graphs.

Submit

12) Which statements are true about trees?

A tree is always connected

A tree always contains exactly one cycle

A tree with n vertices has n−1 edges

Removing any edge disconnects a tree

Trees are connected, acyclic, and minimally connected.

Explanation

Trees are connected, acyclic, and minimally connected.

Submit

13) Match the Following

Path

Cycle

Degree

Paths have no repeated vertices; cycles are closed; degree counts incidents.

Explanation

Paths have no repeated vertices; cycles are closed; degree counts incidents.

Submit

14) Match the Following

Complete graph

Cycle graph

Bipartite graph

Complete=all edges; cycle graph degree 2; bipartite splits vertices.

Explanation

Complete=all edges; cycle graph degree 2; bipartite splits vertices.

Submit

15) Is the degree sequence graphical? 3,3,3,3,4,4,4,4,5,5

Yes

Satisfies Havel–Hakimi / Erdős–Gallai.

Explanation

Satisfies Havel–Hakimi / Erdős–Gallai.

Advanced Graph Terminology and Structural Concepts Quiz

1) A graph consists of:

2)

What first name or nickname would you like us to use?

2) Two vertices connected by an edge are called:

3) In an undirected graph, edges have no orientation.

4) A connected simple graph has 8 vertices. Minimum edges?

5) Which graph cannot be bipartite?

6) The degree of a vertex is:

7) A loop contributes how much to the degree of a vertex?

8) A simple graph has no loops and no multiple edges.

9) A connected graph must contain at least one cycle.

10) A simple graph has 5 vertices and 6 edges. Which must be true?

11) Which of the following are examples of simple graphs?

12) Which statements are true about trees?

13) Match the Following

14) Match the Following

15) Is the degree sequence graphical? 3,3,3,3,4,4,4,4,5,5