Given a graph G, the task is to check if it represents a Star Topology.
A Star Topology is the one shown in the image below:
Input : Graph = Output : YES Input : Graph = Output : NO
A graph of V vertices represents a star topology if it satisfies the following three conditions:
- One node (also called the central node) has degree V – 1.
- All nodes except the central node have degree 1.
- No of edges = No of Vertices – 1.
The idea is to traverse the graph and check if it satisfies the above three conditions. If yes, then it represents a Star Topology.
Below is the implementation of the above approach:
Time Complexity: O(V + E) where V and E are the numbers of vertices and edges in the graph respectively.
- Check if the given graph represents a Bus Topology
- Check if the given graph represents a Ring Topology
- Check for star graph
- Check whether a given graph is Bipartite or not
- Check if a given graph is Bipartite using DFS
- Check if a given graph is tree or not
- Check if the given permutation is a valid DFS of graph
- Check if a given tree graph is linear or not
- Check if a directed graph is connected or not
- Check if removing a given edge disconnects a graph
- Check if there is a cycle with odd weight sum in an undirected graph
- Check if a graph is strongly connected | Set 1 (Kosaraju using DFS)
- Check if a given directed graph is strongly connected | Set 2 (Kosaraju using BFS)
- Two Clique Problem (Check if Graph can be divided in two Cliques)
- Check whether given degrees of vertices represent a Graph or Tree
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