Question 1

What does an adjacency matrix represent in graph theory?

Accepted Answer

The connections between vertices in a graph.

Answer

The length of the edges in a graph.

Answer

The total degree of the graph.

Answer

The number of vertices in a graph.

Question 2

In a graph, what is meant by the degree of a vertex?

Accepted Answer

The number of edges connected to the vertex.

Answer

The total number of vertices in the graph.

Answer

The sum of all weights on edges connected to that vertex.

Answer

The distance from that vertex to another.

Question 3

What is an isomorphic graph?

Accepted Answer

Graphs that have the same structure but may have different representations or labels.

Answer

Graphs with different numbers of vertices.

Answer

Graphs that are completely different.

Answer

Graphs that cannot be represented in matrix form.

Question 4

What is the relationship between the number of edges and the sum of the degrees of all vertices in a graph?

Accepted Answer

The number of edges is half the sum of the degrees of the vertices.

Answer

The number of edges is twice the sum of the degrees of the vertices.

Answer

The number of edges is unrelated to the sum of the degrees of the vertices.

Answer

The number of edges is equal to the sum of the degrees of the vertices.

Question 5

What is the significance of identifying isomorphic graphs?

Accepted Answer

It helps to understand if two different graphs represent the same structure.

Answer

It shows the number of vertices in each graph.

Answer

It allows for the comparison of edge weights.

Answer

It determines the shortest path in a graph.

Question 6

In a graph, what does the term 'connected' refer to?

Accepted Answer

There is a path between any two vertices in the graph.

Answer

The graph includes cycles.

Answer

The graph contains at least one edge.

Answer

All vertices have the same degree.

Question 7

What shape is commonly used to represent a graph's vertices and edges in drawings?

Accepted Answer

Circles for vertices and lines for edges.

Answer

Squares for vertices and dots for edges.

Answer

Triangles for vertices and arrows for edges.

Answer

Hexagons for vertices and dashed lines for edges.

Question 8

If a graph has a vertex of degree 0, what does it signify?

Accepted Answer

The vertex is isolated and has no connections to other vertices.

Answer

It is a complete graph.

Answer

It is a cycle graph.

Answer

It contains multiple edges.

Question 9

How are graphs typically represented in mathematical notation?

Accepted Answer

By using vertices and edges, often with diagrams or matrices.

Answer

By using only pictures.

Answer

By using a set of equations.

Answer

By using just numbers.

Question 10

In a graph representing a city map, what would be the vertices and edges?

Accepted Answer

Vertices are locations (like intersections), and edges are the roads connecting them.

Answer

Vertices are distances and edges are the cities.

Answer

Vertices are landmarks and edges are paths.

Answer

Vertices are the roads, and edges are the locations.

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