C++ program to construct graph with certain conditions

In this article, we will discuss a C++ program to construct graphs with certain conditions.

Basic data structures called graphs, which are used to display the relationships between entities. In many applications, it is crucial to build graphs that adhere to particular constraints or requirements. These specifications could include edge weights, structural restrictions, or requirements for connectivity. The aim of this C++ program is the construction of a graph that satisfies specified criteria. The number of vertices, the presence of particular edges, or properties like acyclicity or connectivity may be related to these specifications. Adjacency matrices and adjacency lists are two examples of the graph representation techniques that the program may employ, depending on the constraints and requirements.

Suppose we have two numbers, N and K. Consider the case of an undirected graph with N elements. N vertices satisfy the following conditions. It has the following conditions:

• The graph is simple and linked.
• The vertices have numbers ranging from 1 to N.
• Let M be the number of edges in the graph. For the edges, a number goes from 1 to M, which is the length of the Edge. Additionally, Edge i connects Vertex V[i] and Vertex U[i].
• There are pairs where i < j and their shortest distance is 2 for each K pairs of vertices (i, j).

Example 1:

Let us take an example to illustrate how to construct graph with certain conditions in C++.

Output:

Number of edges: 11
Edge: 1 -> 2
Edge: 1 -> 3
Edge: 1 -> 4
Edge: 1 -> 5
Edge: 1 -> 6
Edge: 1 -> 7
Edge: 2 -> 3
Edge: 2 -> 4
Edge: 2 -> 5
Edge: 2 -> 6
Edge: 2 -> 7

Example 2:

Let us take another example to illustrate how to construct graph with certain conditions in C++.

Output:

Enter number of vertices: 4
Enter number of edges: 3
Enter edge 1 (source destination): 0 1
Enter edge 2 (source destination): 1 2
Enter edge 3 (source destination): 2 3
Graph is connected.
Generated Graph:
Vertex 0 -> 1 
Vertex 1 -> 0 2 
Vertex 2 -> 1 3 
Vertex 3 -> 2