Basics of Graph Theory

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What is a graph in graph theory?

A graph is a collection of vertices (or nodes) and edges that connect pairs of vertices.

What are vertices in a graph?

Vertices, also called nodes, are points in a graph where edges meet.

What are edges in a graph?

Edges are the connections between pairs of vertices in a graph.

What is a directed graph?

A directed graph is a graph in which the edges have a direction, indicated by an arrow.

What is an undirected graph?

An undirected graph is a graph in which the edges have no direction.

What is a weighted graph?

A weighted graph is a graph in which each edge is assigned a weight or cost.

What is a simple graph?

A simple graph is a graph without loops and multiple edges between any two vertices.

What is a complete graph?

A complete graph is a graph in which every pair of vertices is connected by an edge.

What is a path in graph theory?

A path is a sequence of edges that connect a sequence of distinct vertices.

What is a cycle?

A cycle is a path that starts and ends at the same vertex, with all other vertices distinct.

What is a connected graph?

A connected graph is a graph in which there is a path between every pair of vertices.

Define a subgraph.

A subgraph is a graph formed from a subset of the vertices and edges of another graph.

What is a degree of a vertex?

The degree of a vertex is the number of edges incident to it.

What is a bipartite graph?

A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that no two vertices within the same set are adjacent.

What is a tree in graph theory?

A tree is a connected graph with no cycles.





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1. What is a graph in graph theory?

A graph is a collection of vertices (or nodes) and edges that connect pairs of vertices.

A graph is a function from nodes to paths.

A graph is a connection of paths only.

A graph is a visual representation of numbers.

2. What are vertices in a graph?

Vertices, also called nodes, are points in a graph where edges meet.

Vertices are the edges connecting nodes.

Vertices are the weights of the edges.

Vertices are the directed paths in a graph.

3. What are edges in a graph?

Edges are the connections between pairs of vertices in a graph.

Edges are the points where vertices meet.

Edges are the weights assigned to paths.

Edges are the cycles in a graph.

4. What is a directed graph?

A directed graph is a graph in which the edges have a direction, indicated by an arrow.

A directed graph is a graph with no edges.

A directed graph is a simple path with cycles.

A directed graph is a graph only containing loops.

5. What is an undirected graph?

An undirected graph is a graph especially for weighted graphs.

An undirected graph is a graph in which the edges have no direction.

An undirected graph is just a single vertex.

An undirected graph is a graph with self-loops only.

6. What is a weighted graph?

A weighted graph is a graph in which each edge is assigned a weight or cost.

A weighted graph is a graph where each vertex has a weight.

A weighted graph is a graph with directed paths.

A weighted graph assigns weights to each node.

7. What is a simple graph?

A simple graph is a graph without loops and multiple edges between any two vertices.

A simple graph is just a single cycle.

A simple graph is a graph with at least one loop.

A simple graph contains only one vertex and no edges.

8. What is a complete graph?

A complete graph is a graph in which every pair of vertices is connected by an edge.

A complete graph has no edges.

A complete graph only consists of trees.

A complete graph is one that is fully colored.

9. What is a path in graph theory?

A path is a sequence of edges that connect a sequence of distinct vertices.

A path is a cycle in a weighted graph.

A path is a sequence of identical vertices.

A path is a single vertex without edges.

10. What is a cycle?

A cycle is a path that starts and ends at the same vertex, with all other vertices distinct.

A cycle is a graph with no edges.

A cycle is any two nodes with the same edges.

A cycle is a graph that only contains loops.

11. What is a connected graph?

A connected graph contains isolated vertices.

A connected graph is a graph with no vertices.

A connected graph is a graph in which there is a path between every pair of vertices.

A connected graph is always a weighted graph.

12. Define a subgraph.

A subgraph is a graph formed by copying the entire graph.

A subgraph is a cycle within a graph.

A subgraph is a graph formed from a subset of the vertices and edges of another graph.

A subgraph is a single vertex with no edges.

13. What is a degree of a vertex?

The degree of a vertex is the number of edges incident to it.

The degree of a vertex is the number of vertices in the graph.

The degree of a vertex is the total number of paths connected to it.

The degree of a vertex is the total weight of a graph.

14. What is a bipartite graph?

A bipartite graph is a graph with weighted edges only.

A bipartite graph is a graph with all directed cycles.

A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that no two vertices within the same set are adjacent.

A bipartite graph is a graph consisting of only two edges.

15. What is a tree in graph theory?

A tree is a graph that contains exactly three vertices.

A tree is a graph with self-loops.

A tree is a connected graph with no cycles.

A tree is a single vertex without edges.