## Directed Graphs

Degree of Vertex The degree of vertex is the total number of vertices in the graph minus 1 or we can say that the number of vertices adjacent to a vertex V is the degree of vertex. Notation - deg(V). 123  Notation - deg(V).  Degree of vertex can be...

## Planar Graphs

What is a Planar Graph? The graph that can be drawn on a plane such that no two edges cross each other or intersect each other, this type of graph is called planar graph. Such a drawing of a planar graph is called planar embedding of the graph. It divides the plane...

## Coverings in Graph

A covering graph ‘C’ is a subgraph that either contains all the vertices or all the edges of graph ‘G’. Coverings in Graph There are basically two types of Covering: Edge Covering: A subgraph that contains all the edges of graph ‘G’...

## Independent Set

Independent Set In any subset S when the two vertices are not adjacent to each other, such a subset of vertices is called an independent set. A single vertex in any graph is said to be an independent set. Independent set is sometime also known as internally stable...

## Hamiltonian Graph

What is Hamiltonian graph? Hamiltonian graph is a graph in which each vertex is visited exactly once. A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. Sometimes it is also known as Hamilton graph. This graph was named after the scientist...

## Eulerian Graphs

What is Eulerian graph? Eulerian graph or Euler’s graph is a graph in which we draw the path between every vertices without retracing the path. These are undirected graphs. These were first explained by Leonhard Euler while solving the famous Seven Bridges of...

## Trees in Graph

What is tree? A tree is an undirected graph in which two vertices are connected together by exactly one path. A tree with N number of vertices contains (N−1) number of edges. The edges of a tree are known as branches. Elements of trees are called their nodes. The...

## Connected Graphs

What is connected graph? A connected graph is a graph in which there is an edge between every pair of vertices. It means, we can travel from any point to any other point in the graph. What is disconnected graph? A graph G is said to be disconnected if there is no edge...

## Types of Graph

1. Null Graph: The graph which has no edges is known as Null Graph. Sometime it is also known as empty graph or edgeless graph. For example: 2. Trivial Graph: The graph which has only one vertex is known as Trivial Graph. For example: 3. Non-Directed Graph: These are...

## Graph Theory Introduction

Simple Terminologies used in Graph Theory What is Graph? A Graph is a connection of lines and points which represents a network. A graph ‘G’ is a set of vertices called nodes. Vertices are denoted by ‘v’ which are connected by edges called...