How do you prove the chromatic number of a graph?

Chromatic Number: The chromatic number of a graph G is the least k for which a k-coloring of G exists. Thus if a graph G has chromatic number k, then G has a k-coloring, but not a (k-1)-coloring. For example a path has chromatic number 2, while the complete graph Kn has chromatic number n.

What will be the number of edges in a complete graph consisting of 4 notes?

A complete graph has an edge between any two vertices. You can get an edge by picking any two vertices. So if there are n vertices, there are n choose 2 = (n2)=n(n−1)/2 edges.

What is the chromatic number of the following graph?

3
Explanation: Chromatic number of given graph is 3.

What is a 4 regular graph?

In the mathematical field of graph theory, a quartic graph is a graph where all vertices have degree 4. In other words, a quartic graph is a 4-regular graph.

How do you make sure a graph is connected?

A simple solution is to perform Depth–first search (DFS) or Breadth–first search (BFS) starting from every vertex in the graph. If each DFS/BFS call visits every other vertex in the graph, then the graph is strongly connected. The algorithm can be implemented as follows in C++, Java, and Python: C++

How do you find the edge of a graph?

The number of edges connected to a single vertex v is the degree of v. Thus, the sum of all the degrees of vertices in the graph equals the total number of incident pairs (v, e) we wanted to count. For the second way of counting the incident pairs, notice that each edge is attached to two vertices.

How many edges are there in a complete graph?

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.