Fundamentals of Graph Terminology Quiz

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Ekaterina Yukhnovich, PhD |
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Ekaterina V. is a physicist and mathematics expert with a PhD in Physics and Mathematics and extensive experience working with advanced secondary and undergraduate-level content. She specializes in combinatorics, applied mathematics, and scientific writing, with a strong focus on accuracy and academic rigor.
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| Attempts: 13 | Questions: 15 | Updated: Dec 16, 2025
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1) A graph with no edges is called a:

Explanation

A null graph has only isolated vertices.

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About This Quiz
Fundamentals Of Graph Terminology Quiz - Quiz

Are you ready to explore the building blocks of graph theory? This quiz introduces the essential terms that describe how graphs work — from vertices and edges to walks, trails, cycles, leaves, and complete structures. You’ll learn how graphs are classified, how degrees are defined, and what makes a graph... see moresimple, connected, or bipartite. With clear examples involving paths, tree structures, and graph complements, you’ll develop a strong foundation for recognizing how graphs represent networks, relationships, and connections all around us. Get ready to strengthen your understanding of one of the most important areas in discrete mathematics!
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2) Two edges sharing a common vertex are called adjacent edges.

Explanation

Adjacent edges meet at a shared vertex.

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3) A graph is called simple if it:

Explanation

Simplicity means no repeated edges or loops.

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4) The number of edges in a graph is called its:

Explanation

Size = number of edges.

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5) A complete graph is one where every pair of distinct vertices is connected by an edge.

Explanation

That is the definition of a complete graph.

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6) Vertices that have degree 1 are called:

Explanation

A degree-1 vertex is a leaf.

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7) A connected graph with no cycles is called a:

Explanation

A tree is acyclic and connected.

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8) In a simple graph, two vertices with the same degree are called:

Explanation

Vertices with equal degree may be referred to as twins.

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9) The complement of a simple graph is the graph that:

Explanation

The complement contains exactly the missing edges.

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10) The number of vertices in a graph is called its:

Explanation

Order = number of vertices.

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11) A walk in a graph allows:

Explanation

Walks may repeat vertices and edges.

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12) A trail is a walk with:

Explanation

Trails cannot repeat edges.

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13) A cycle is a closed walk with no repeated edges and no repeated vertices (except start/end).

Explanation

A cycle returns to its start without repeating internal vertices.

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14) Which graphs are always bipartite?

Explanation

Odd cycles are not bipartite.

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15) A spanning subgraph contains all vertices of the original graph.

Explanation

“Spanning” means including every vertex.

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Ekaterina Yukhnovich |PhD |
College Expert
Ekaterina V. is a physicist and mathematics expert with a PhD in Physics and Mathematics and extensive experience working with advanced secondary and undergraduate-level content. She specializes in combinatorics, applied mathematics, and scientific writing, with a strong focus on accuracy and academic rigor.
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A graph with no edges is called a:
Two edges sharing a common vertex are called adjacent edges.
A graph is called simple if it:
The number of edges in a graph is called its:
A complete graph is one where every pair of distinct vertices is...
Vertices that have degree 1 are called:
A connected graph with no cycles is called a:
In a simple graph, two vertices with the same degree are called:
The complement of a simple graph is the graph that:
The number of vertices in a graph is called its:
A walk in a graph allows:
A trail is a walk with:
A cycle is a closed walk with no repeated edges and no repeated...
Which graphs are always bipartite?
A spanning subgraph contains all vertices of the original graph.
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