Table of Contents

## How do you know if two graphs are isomorphic?

You can say given graphs are isomorphic if they have:

- Equal number of vertices.
- Equal number of edges.
- Same degree sequence.
- Same number of circuit of particular length.

## What does it mean for two graphs to be isomorphic?

Two graphs which contain the same number of graph vertices connected in the same way are said to be isomorphic. Formally, two graphs and with graph vertices are said to be isomorphic if there is a permutation of such that is in the set of graph edges iff is in the set of graph edges .

**What is isomorphic determine the following graphs are isomorphic or not?**

Two graphs are isomorphic if and only if their complement graphs are isomorphic. Two graphs are isomorphic if their adjacency matrices are same. Two graphs are isomorphic if their corresponding sub-graphs obtained by deleting some vertices of one graph and their corresponding images in the other graph are isomorphic.

### How can you prove a graph is not isomorphic?

To show that two graphs are not isomorphic, you must show that here exists no such mapping between the vertices. This can be a tricky thing to do, but sometimes there’s an easier way. Isomorphic graphs necessarily share certain properties.

### What is the number of vertices in an undirected graph with 39 edges?

What is the number of vertices in an undirected connected graph with 39 edges, 7 vertices of degree 2, 2 vertices of degree 5 and remaining of degree 6? Number of vertices = 7 + 2 + 9 = 18.

**What is the maximum number of edges in an acyclic undirected graph with n vertices?**

What is the maximum number of edges in an acyclic undirected graph with n vertices? Explanation: n * (n “ 1) / 2 when cyclic. But acyclic graph with the maximum number of edges is actually a spanning tree and therefore, correct answer is n-1 edges.

## What is the maximum number of edges in an undirected graph with n vertices?

The maximum number of edges in an undirected graph is n(n-1)/2 and obviously in a directed graph there are twice as many. If the graph is not a multi graph then it is clearly n * (n – 1), as each node can at most have edges to every other node. If this is a multigraph, then there is no max limit.

## How many vertices does a 4 graph with 10 edges have?

5

**How many edges will be there in a 3 regular graph of 6 vertices?**

For 3 vertices the maximum number of edges is 3; for 4 it is 6; for 5 it is 10 and for 6 it is 15. For n,N=n(nˆ’1)/2. There are two ways at least to prove this.

### What is the maximum degree of any vertex in a simple graph with n vertices?

A simple graph has no loops or parallel edges. So, out of the total n vertices, all the vertices except the vertex itself (n-1 vertices) can be adjacent (have an edge) to this vertex. So, it’s degree can be maximum n-1.

### Which of the following is true 1 a graph may contain no edges and many vertices 2 a graph may contain many edges and no vertices 3 a graph may contain no edges and no vertices 4 a graph may contain no vertices?

a) A graph may contain no edges and many verticesb) A graph may contain many edges and no verticesc) A graph may contain no edges and no verticesd) None of the mentionedAnswer: aExplanation: A graph must contain at least one vertex. 24.

**What is the number of vertices of degree 2 in a path graph having n vertices?**

What is the number of vertices of degree 2 in a path graph having n vertices,here n>2. Explanation: Only the first and the last vertex would have degree 1, others would be of degree 2. 7. All trees with n vertices consists of n-1 edges.

## How many edges are present in a complete graph with n vertices?

2 edges

## How many nodes are necessary to construct a graph with exactly 6 edges?

6 nodes

**How many edges are there in a graph with 10 vertices with degree 6?**

60

### What is the maximum number of edges in an undirected graph with eight vertices?

28

### What is the number of unlabeled simple directed graph that can be made with one or two vertices?

Discussion Forum

Que. | What is the number of unlabeled simple directed graph that can be made with 1 or 2 vertices? |
---|---|

b. | 4 |

c. | 5 |

d. | 9 |

Answer:4 |

**What is the maximum number of edges in a directed graph without self loops having 8 vertices?**

Discussion Forum

Que. | What is the maximum possible number of edges in a directed graph with no self loops having 8 vertices? |
---|---|

b. | 64 |

c. | 256 |

d. | 56 |

Answer:56 |

## How do you know how many edges a graph has?

1 Answer. The sum of the vertex degree values is twice the number of edges, because each of the edges has been counted from both ends. In your case 6 vertices of degree 4 mean there are (6Ã—4)/2=12 edges.

## How do you find the number of edges in a regular graph of degree d and n vertices?

Regular graph, a graph in which all vertices have same degree. example:- if n=3 and d=2 so there are 3*2/2 = 3 edges. if n=4 and d=2 so there are 4*2/2 = 4 edges. and so on.

**Which of the following is not an advantage of trees?**

Which of the following is not an advantage of trees? Explanation: Undo/Redo operations in a notepad is an application of stack. Hierarchical structure, Faster search, Router algorithms are advantages of trees. 7.