What is the largest number of vertices in a graph with 35 edges?
What is the largest number of vertices in a graph with 35 edges if all vertices are of degree at least 3? I thought up of a solution but there are some questions I could not find. So the largest number of vertices are 23, with the given constraints.
How many edges can a graph with n vertices have?
2 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). There can be as many as n(n-1)/2 edges in the graph if not multi-edge is allowed.
Can a simple graph with 8 vertices have 40 edges?
8(8-1) / 2 = 28. Therefore a simple graph with 8 vertices can have a maximum of 28 edges.
What is the largest number of vertices in a graph with 35 edges if all vertices are of degree at least 3 Why?
Which means, Each edge contributes twice to the sum of the degrees of all vertices. Now, the graph has 35 Edges. ∴ 2×Edges=2×35=70 is the Maximum Sum of degree of the vertices.
What is the maximum number of vertices in a graph with 25 edges and all vertices are of degree at least 4?
Detailed Solution. So, maximum possible value of n is 16.
How many vertices does a graph contain if it has 21 edges 3 vertices each of degree 4 and other vertices each of degree 3?
∴ Number of vertices in the graph is 18.
How many vertices will a graph have if it contains 21 edges 3 vertices of degree 4 and other vertices of degree 3?
A simple non directed graph contains 21 edges, 3 vertices of degree 4 and the other vertices are of degree 2….Subscribe to GO Classes for GATE CSE 2022.
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How many vertices are there in complete graph with n vertices?
Definition: A complete graph is a graph with N vertices and an edge between every two vertices.
How many edges are there in a complete graph on 9 vertices?
A complete graph is a graph in which every pair of vertices is connected by exactly one edge. So a complete graph on n vertices contains n(n – 1)/2 edges and your question is equivalent to asking what value of n makes n(n – 1)/2 = 45. 10 x 9/2 = 45 so the answer is 10.
How many vertices does the graph G have?
A graph G has 50 edges and 30 vertices. Each vertex in G has either degree 3 or degree 4. How many of the 30 vertices in G have degree 3 and how many have degree 4?
How many edges does a non-connected graph have to have?
The non-connected graph on n vertices with the most edges is a complete graph on $n-1$ vertices and one isolated vertex. So you must have $ 1+ {\\frac{n(n-1)}{2} \\space}$ edges to guarantee connectedness.
How do you find the minimum number of edges needed for connectivity?
Hence, as you correctly calculate, there are ( n 2) = ( n − 1) ( n − 2) 2 edges. Adding any possible edge must connect the graph, so the minimum number of edges needed to guarantee connectivity for an n vertex graph is ( n − 1) ( n − 2) 2 + 1.
What is the sum of the degrees of all the vertices?
If there are 50 edges, the sum of the degrees of all the vertices should be twice that number at 100. Call the number of vertices of degree 3 x. There are then 30 − x vertices of degree 4. I get a sense this might be homework, so I’ll leave the algebra of solving for x to you.