Given an undirected graph G(V, E) with N vertices and M edges. We need to find the minimum number of edges between a given pair of vertices (u, v).
We have already discussed this problem using the BFS approach, here we will use the DFS approach.
Input: For the following given graph, find the minimum number of edges between vertex pair (0, 4)
There are three paths from 0 to 4:
0 -> 1 -> 2 -> 4
0 -> 1 -> 2 -> 3 -> 4
0 -> 4
Only the third path results in minimum number of edges.
Approach: In this approach we will traverse the graph in a DFS manner, starting from the given vertex and explore all the paths from that vertex to our destination vertex.
We will use two variables, edge_count and min_num_of_edges. While exploring all the paths, between these vertices, edge_count will store count of total number of edges among them, if number of edges is less than the minimum number of edges we will update min_num_of_edges.
Below is the implementation of the above approach:
- Minimum number of edges between two vertices of a Graph
- Number of Simple Graph with N Vertices and M Edges
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- Calculate number of nodes between two vertices in an acyclic Graph by Disjoint Union method
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- Finding in and out degrees of all vertices in a graph
- Find if there is a path between two vertices in a directed graph
- All vertex pairs connected with exactly k edges in a graph
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