Given a graph with n nodes and m edges. Find the maximum possible number of nodes which are not part of any edge (m will always be less than or equal to a number of edges in complete graph).
Input: n = 3, m = 3 Output: Maximum Nodes Left Out: 0 Since it is a complete graph. Input: n = 7, m = 6 Output: Maximum Nodes Left Out: 3 We can construct a complete graph on 4 vertices using 6 edges.
Approach: Iterate over all n and see at which a number of nodes if we make a complete graph we obtain a number of edges more than m say it is K. Answer is n-k.
- Maximum number of edges which can be used to form a graph on n nodes is n * (n – 1) / 2 (A complete Graph).
- Then find number of maximum n, which will use m or less than m edges to form a complete graph.
- If still edges are left, then it will cover only one more node, as if it would have covered more than one node than, this is not the maximum value of n.
Below is the implementation of above approach:
- Edge Coloring of a Graph
- Check if removing a given edge disconnects a graph
- Program to Calculate the Edge Cover of a Graph
- Number of sink nodes in a graph
- Tree, Back, Edge and Cross Edges in DFS of Graph
- Shortest Path in a weighted Graph where weight of an edge is 1 or 2
- Maximum Possible Edge Disjoint Spanning Tree From a Complete Graph
- Maximum number of nodes which can be reached from each node in a graph.
- Paths to travel each nodes using each edge (Seven Bridges of Königsberg)
- Calculate number of nodes between two vertices in an acyclic Graph by Disjoint Union method
- Detect cycle in the graph using degrees of nodes of graph
- Sum of degrees of all nodes of a undirected graph
- Find maximum number of edge disjoint paths between two vertices
- Check if given path between two nodes of a graph represents a shortest paths
- Kth largest node among all directly connected nodes to the given node in an undirected graph
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