cycle graph
graph that includes every vertex in which every vertex is adjacent to exactly 2 vertices
A cycle graph is a type of graph in which a single closed loop is formed. It is also known as a circular graph or a cycle. A cycle graph can be represented by a circle, in which the vertices are the points on the circle, and the edges are the arcs between these points.
The number of vertices in a cycle graph is denoted by n. Thus, a cycle graph with n vertices is denoted by Cn. A cycle graph with 3 vertices is called a triangle, while a cycle graph with 4 vertices is called a square or a quadrilateral.
Some properties of cycle graphs are:
– The degree of each vertex in a cycle graph is 2, since each vertex is connected to exactly two other vertices.
– The cycle graph Cn has n edges.
– The shortest path between any two vertices in a cycle graph is the length of the arc between them. Thus, the shortest path in Cn between two vertices that are k spaces apart is min(k, n-k).
– The diameter of a cycle graph with n vertices is n/2 if n is even, or (n+1)/2 if n is odd.
Cycle graphs are used in various applications such as in chemistry, where they are used to represent cyclic molecules, and in computer science, where they are used in algorithms for cycle detection and optimization.
More Answers:
[next_post_link]