Given the number of vertices in a Cycle Graph. The task is to find the Degree and the number of Edges of the cycle graph.
Degree: Degree of any vertex is defined as the number of edge Incident on it.
Cycle Graph: In graph theory, a graph that consists of single cycle is called a cycle graph or circular graph. The cycle graph with n vertices is called Cn.
Properties of Cycle Graph:-
- It is a Connected Graph.
- A Cycle Graph or Circular Graph is a graph that consists of a single cycle.
- In a Cycle Graph number of vertices is equal to number of edges.
- A Cycle Graph is 2-edge colorable or 2-vertex colorable, if and only if it has an even number of vertices.
- A Cycle Graph is 3-edge colorable or 3-edge colorable, if and only if it has an odd number of vertices.
- In a Cycle Graph, Degree of each vertx in a graph is two.
- The degree of a Cycle graph is 2 times the number of vertices. As each edge is counted twice.
Input: Number of vertices = 4 Output: Degree is 8 Edges are 4 Explanation: The total edges are 4 and the Degree of the Graph is 8 as 2 edge incident on each of the vertices i.e on a, b, c, and d. Input: number of vertices = 5 Output: Degree is 10 Edges are 5
Below is the implementaion of the above problem:
Program 1: For 4 vertices cycle graph
For numberOfVertices = 4 Degree = 8 Number of Edges = 4
Program 2: For 6 vertices cycle graph
For numberOfVertices = 6 Degree = 12 Number of Edges = 6
- Find the Degree of a Particular vertex in a Graph
- Coloring a Cycle Graph
- Detect Cycle in a Directed Graph using BFS
- Detect cycle in an undirected graph using BFS
- Detect cycle in an undirected graph
- Detect Cycle in a Directed Graph
- Detect Cycle in a directed graph using colors
- Check if there is a cycle with odd weight sum in an undirected graph
- Detect a negative cycle in a Graph | (Bellman Ford)
- Find minimum weight cycle in an undirected graph
- Total number of Spanning trees in a Cycle Graph
- Number of single cycle components in an undirected graph
- Disjoint Set (Or Union-Find) | Set 1 (Detect Cycle in an Undirected Graph)
- Graph implementation using STL for competitive programming | Set 2 (Weighted graph)
- Hamiltonian Cycle | Backtracking-6
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