Cycle graph

A circle graph, short circuit, in graph theory is a class of graphs of simple structure. A circle graph always has the same number of nodes as edges, all nodes are connected to each other in a circle. Circle graph with vertices are denoted by. A network topology in the form of a circle graph is called a ring topology.

Definition

A circle graph is an undirected graph consisting of the nodes

And edges

Which is usually assumed. A circle graph with nodes is also called the circuit or cycle.

Properties

Below are just a circle graph are considered to consist of at least three nodes.

• All circle graphs are connected, planar, cyclic, Euler tour and hamiltonian.
• All circle graphs are 2 -regular, ie, each node has degree two.
• The edge graph of the circuit graph is isomorphic to its output graph, so again a circle graph with nodes.
• The diameter and the number of circuit stability graph.
• The chromatic number of circle graphs is two if just is three and if is odd.
• The chromatic polynomial of circle graphs.
• All circle graphs are homeomorphic for each other.

Features special circle graphs are:

• The circle graph is a special triangulation.
• The circle graph is a special grid graph.
• The circle graph is the smallest regular graph that is not strongly regular.