How many vertices does a tree with 17 edges have?

17 edges means 34 edge-vertex incidences.

What is the maximum number of vertices in a connected graph of n edges?

In a directed graph having N vertices, each vertex can connect to N-1 other vertices in the graph(Assuming, no self loop). Hence, the total number of edges can be are N(N-1).

How many vertices does a connected graph have?

A graph with just one vertex is connected. An edgeless graph with two or more vertices is disconnected. A directed graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph.

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What is the maximum number of edges in a simple graph with 15 vertices?

The maximum number of edges possible in a single graph with ‘n’ vertices is nC2 where nC2 = n(n – 1)/2. The number of simple graphs possible with ‘n’ vertices = 2nc2 = 2n(n-1)/2.

How many Hamilton circuits are in a graph with 8 vertices?

5040 possible Hamiltonian circuits
A complete graph with 8 vertices would have = 5040 possible Hamiltonian circuits.

How many vertices does a tree have?

A labeled tree with 6 vertices and 5 edges. In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph.

What is the maximum number of vertices?

Cuboid has the maximum number of vertices. Hence, option (c) Cuboid is the correct answer.

How do you find the maximum number of vertices?

We know that e1+e2+e3+e4+e5=40 so there can be 45 vertices maximum.

How many vertices are there in a graph with 16 edges if each vertex is of degree 4?

two vertices
Answer and Explanation: Given that a graph g has 16 edges, two vertices of degree 4 , two of degree 1 and the remaining vertices…

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How many edges does a connected graph have?

The minimum number of edges for undirected connected graph is (n-1) edges. To see this, since the graph is connected then there must be a unique path from every vertex to every other vertex and removing any edge will make the graph disconnected.

How many Hamilton circuits are in a graph with 9 vertices?

Example16.3

Number of vertices Number of unique Hamilton circuits
6 60
7 360
8 2520
9 20,160

What is the maximum number of edges a graph can have?

The maximum number of edges is simply the number of pairs of distinct vertices; if there are n vertices, this is ( n 2) = n! 2! ( n − 2)! = n ( n − 1) 2. Thanks for contributing an answer to Mathematics Stack Exchange!

How do you find the maximum number of vertices a component can have?

A component should have at least 1 vertex, so give 1 vertex to the k-1 components. Now n- (k-1) = n-k+1 vertices remain. For the maximum edges, this large component should be complete. Maximum edges possible with n-k+1 vertex = ( n − k + 1 2) = ( n − k + 1) ( n − k) 2

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How do you join two components with more than one vertex?

Then there exist two components with more than one vertex say the number of vertices are \$n\$ and \$m\$ . Pick the one with the less vertices suppose it is \$m\$ vertices. Take one of it vertices and delete it. removing \$m-1\$ edges. now add a new vertex to the component with \$n\$ vertices and join it to all its vertices, adding \$n\$ edges.

How many components does a graph have that is not connected?

Since the graph is not connected it has at least two components. Even if it has more than 2 components, you can think about it as having 2 “pieces”, not necessarily connected. Let k and n − k be the number of vertices in the two pieces.