Advanced Graph Terminology and Structural Concepts Quiz

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Quizzes Created: 7682 | Total Attempts: 9,547,133
| Attempts: 13 | Questions: 15 | Updated: Dec 12, 2025
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Question 1 / 15
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1) A graph consists of:

Explanation

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

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About This Quiz
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)
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2) Two vertices connected by an edge are called:

Explanation

Adjacent means joined by an edge.

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3) The degree of a vertex is:

Explanation

Degree counts incident edges.

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

Explanation

A loop touches the vertex twice.

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

Explanation

Simplicity prohibits both loops and parallel edges.

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

Explanation

Undirected edges do not point from one vertex to another.

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

Explanation

Trees are connected and acyclic.

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

Explanation

Loops and parallel edges are not allowed in simple graphs.

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9) Which statements are true about trees?

Explanation

Trees are connected, acyclic, and minimally connected.

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10) Match the Following

Explanation

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

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11) Match the Following

Explanation

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

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

Explanation

Total degree=12 ⇒ avg=2.4 ⇒ some ≥3.

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

Explanation

A tree with 8 vertices has 7 edges.

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14) Which graph cannot be bipartite?

Explanation

Odd cycles are not bipartite.

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

Explanation

Satisfies Havel–Hakimi / Erdős–Gallai.

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A graph consists of:
Two vertices connected by an edge are called:
The degree of a vertex is:
A loop contributes how much to the degree of a vertex?
A simple graph has no loops and no multiple edges.
In an undirected graph, edges have no orientation.
A connected graph must contain at least one cycle.
Which of the following are examples of simple graphs?
Which statements are true about trees?
Match the Following
Match the Following
A simple graph has 5 vertices and 6 edges. Which must be true?
A connected simple graph has 8 vertices. Minimum edges?
Which graph cannot be bipartite?
Is the degree sequence graphical? 3,3,3,3,4,4,4,4,5,5
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