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Understanding Graph Theory

Total questions: 13

Worksheet time: 7mins

Name
Class
Date
1.

What is a graph in graph theory?

a)

A type of function plot

b)

A chart used in statistics

c)

A 3D model in computer graphics

d)

A collection of vertices and edges

2.

What does it mean if a graph is 'complete'?

a)

It has an edge from every vertex to every other vertex

b)

It is fully colored

c)

It contains no edges

d)

It only has vertices and no edges

3.

What is an 'empty graph'?

a)

A graph with only one vertex

b)

A graph that is not connected

c)

A graph with vertices but no edges

d)

A graph with no vertices and no edges

4.

What is the 'order' of a graph?

a)

The maximum degree of the graph

b)

The number of vertices in the graph

c)

The number of edges in the graph

d)

The sequence of vertices

5.

What is a 'directed graph'?

a)

A graph where each edge has a direction

b)

A graph where edges are bidirectional

c)

A graph with no directions on edges

d)

A graph that can only be drawn straight

6.

What does 'isomorphic' mean in the context of graphs?

a)

Two graphs having the same structure

b)

Graphs that are colored the same

c)

Graphs that are completely different

d)

Graphs that have identical vertices

7.

What is a 'tree' in graph theory?

a)

A directed graph with one way edges

b)

An undirected graph with no cycles

c)

A complete graph

d)

A graph with only one vertex

8.

What is an Eulerian path?

a)

A path that starts and ends at the same vertex

b)

A path that can be traversed in both directions

c)

A path that visits every vertex once

d)

A path that crosses every edge exactly once

9.

What challenge did Euler solve about the Koenigsberg bridges?

a)

Calculated the shortest path across all bridges

b)

Designed new bridges to make the path possible

c)

Found a path that crossed each bridge twice

d)

Proved that a path crossing each bridge once is impossible unless each vertex has an even degree

10.

What is a Hamiltonian path?

a)

A path that includes at least one cycle

b)

A path that uses the shortest possible route

c)

A path that crosses each edge exactly once

d)

A path that visits each vertex exactly once

11.

What is a 'bipartite graph' in graph theory?

a)

A graph that can be colored using two colors such that no two adjacent vertices share the same color

b)

A graph where each vertex is connected to all other vertices

c)

A graph with vertices of only two types

d)

A graph that contains exactly two vertices

12.

What does a 'weighted graph' imply in graph theory?

a)

A graph where edges have directions

b)

A graph where each edge has a numerical value associated with it

c)

A graph that is heavier than usual

d)

A graph used in weightlifting competitions

13.

What is the 'degree' of a vertex in a graph?

a)

The number of edges connected to the vertex

b)

The maximum distance to another vertex

c)

The number of graphs it belongs to

d)

The direction of edges connected to the vertex