Given the number of Vertices and the number of Edges of an Undirected Graph. The task is to determine the Circuit rank.
Circuit Rank: The Circuit rank of an undirected graph is defined as the minimum number of edges that must be removed from the graph to break all of its cycles, converting it into a tree or forest.
Input : Edges = 7 , Vertices = 5 Output : Circuit rank = 3 Input : Edges = 7 , Vertices = 6 Output : Circuit rank = 2
Circuit rank = Edges - (Vertices - 1)
Look at the sample graph below,
Total number of Edges = 7 and Vertices = 5.
According to the above formula,
Circuit Rank = Edges - (Vertices - 1) = 7 - (5 - 1) = 3
Therefore, Circuit Rank of the above graph = 3.
It can be seen in the below image that by removing 3 edges(a-d, a-e, c-d) from the above graph, all of it cycles can be removed.
Below is the implementation of the above approach:
Circuit Rank = 3
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- Convert the undirected graph into directed graph such that there is no path of length greater than 1
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- Clone an Undirected Graph
- Detect cycle in an undirected graph
- Sum of degrees of all nodes of a undirected graph
- Number of Triangles in an Undirected Graph
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- Connected Components in an undirected graph
- Detect cycle in an undirected graph using BFS
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