Degree of a Cycle Graph

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 vertex in a graph is two.
• The degree of a Cycle graph is 2 times the number of vertices. As each edge is counted twice.

Examples:  

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. 

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Input: number of vertices = 5
Output: Degree is 10
 Edges are 5

Below is the implementation 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