- Trivial Graph
- Complete Graph
- Regular Graph
- Bipartite Graph
- Complete Bipartite Graph
- Cycle Graph
- Wheel Graph
- Platonic Graph

## ‣ Trivial Graph:

A **trivial graph **is a graph with only one vertex and no edges. It is the simplest possible graph.

**Figure**:

## ‣ Complete Graph:

A graph G is said to be **complete **if there exists exactly one edge between any pair of vertices in G.

• The complete graph with **n **vertices is denoted by **k _{n}**.

## ‣ Regular Graph:

A graph is **regular **if all the vertices of the graph have the same degree. In a regular graph G of degree r, the degree of each vertex of G is **r**.

• In above figure, k2, k3, k4, k5, k6, k7 are 2-regular,

## ‣ Bipartite Graph:

A **bipartite graph **is a graph in which the vertices can be divided into two sets, such that every edge connects a vertex in one set to a vertex in the other set.

• In above figure, **bipartite sets **are: {1,2,3,4,5} and {A,B,C,D,E}

## ‣ Complete Bipartite Graph:

A **complete bipartite graph** is a bipartite graph in which each vertex in the first set is joined to every single vertex in the second set. The complete bipartite graph is denoted by K_{m,n} where the graph G contains m vertices in the first set and x vertices in the second set.

## ‣ Cycle Graph:

A **cycle graph** is a graph that consists of a single cycle. In other words, it is a graph in which every vertex is connected to exactly two other vertices, and there are no edges that connect vertices that are already connected by another edge.

• Each vertex in the above figure is connected to exactly two other vertices by edges.

## ‣ Wheel Graph:

A **wheel graph **is a graph that consists of a single vertex connected to all other vertices in the graph by an edge. The other vertices in the graph are called the rim of the wheel.

• The vertex in the center of the diagram is the **hub of the wheel**, and the other vertices are the **rim of the wheel.**

## ‣ Platonic Graph:

The graph formed by the vertices and edges of **five regular platonic**– the tetrahedron, octahedron, cube, dodecahedron, and icosahedron are called **the platonic graphs**.