What are different types of graphs in discrete mathematics?

In discrete mathematics, a graph is a collection of points, called vertices, and lines between those points, called edges. There are many different types of graphs, such as connected and disconnected graphs, bipartite graphs, weighted graphs, directed and undirected graphs, and simple graphs.

What is finite graph in discrete mathematics?

A finite graph is a graph in which the vertex set and the edge set are finite sets. Otherwise, it is called an infinite graph. Most commonly in graph theory it is implied that the graphs discussed are finite. If the graphs are infinite, that is usually specifically stated.

What is pseudo graph in graph theory?

A pseudograph is a non-simple graph in which both graph loops and multiple edges are permitted (Zwillinger 2003, p. 220). SEE ALSO: Graph Loop, Hypergraph, Multigraph, Multiple Edge, Reflexive Graph, Simple Graph. REFERENCES: Harary, F.

What is bipartite graph example?

A Bipartite Graph is a graph whose vertices can be divided into two independent sets, U and V such that every edge (u, v) either connects a vertex from U to V or a vertex from V to U. For example, see the following graph. It is not possible to color a cycle graph with odd cycle using two colors.

Is null graph a simple graph?

Null Graph: A graph of order n and size zero that is a graph which contain n number of vertices but do not contain any edge. Complete Graph: A simple graph with n vertices is called a complete graph if the degree of each vertex is n-1, that is, one vertex is attach with n-1 edges.

What is the difference between pseudo graph and multigraph?

a multigraph (in contrast to a simple graph) is a graph which is permitted to have multiple edges (also called parallel edges), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge. a pseudograph is a multigraph that is permitted to have loops.

What does bipartite mean discrete mathematics?

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent.

Is Petersen graph connected?

As a connected bridgeless cubic graph with chromatic index four, the Petersen graph is a snark. It is the smallest possible snark, and was the only known snark from 1898 until 1946.

Is the Petersen graph bipartite?

The Petersen graph contains odd cycles – it is not bipartite. The Petersen graph contains a subdivision of K3,3, as shown below, so it is not planar.