Discrete structures/Mathematics (Graph-2)

Now after vertices and edges we will be dealing with some more concepts.

Loop- The edge which starts and ends at same node/vertex is called a loop

                                                  

                                 In above figure the edge starts and ends at the same point

Their are two types of graphs based on direction

a) Directed Graph- The graph which has direction in its edges is called directed graph
                                     
                                      The arrowheads shows the direction of the edges

b) Non-directed/Undirected Graph- The graph which has no direction in its edges is called                                                              undirected/non-directed graph.
                                      
                                      Note that here their are no arrowheads in the edges

Discrete Structures/Mathematics(Graph-1)

What is a Graph?

The graph can be defined in many ways 

 a) A graph is a collection of vertices and edges.

 b) A graph $G=(V,E)$ is a non-empty set of vertices  V and a set of edges E.

 c) A graph G=(V,E) consist of following parts
     (i) A set V=V(G) whose elements are called vertices or nodes.
     (ii) A collection E=E(G) of unordered pair of distinct vertices called edges.

Degree of a Vertex − The degree of a vertex V of a graph G denoted by deg(V) is the number of edges incident with the vertex V.



***For better understanding consider the following example
Here we are going to find the DEGREE OF VERTEX

The degree of the vertex is depected infront of the its name
Vertex                                    Degree

a                                                2

b                                                2

c                                                3

                                                             d                                                1

Discrete Structures/Mathematics (Graph Theory Basics)

Basic points to be known before starting Graph Theory

1.  Vertices - Vertex is referred to the corner most in a Graph.
2.  Edges - Edge is a line that joins two vertices.

The figure shows the Vertices(Nodes) and edges(Links) 

Discrete Structures/Mathematics (Introduction to Subject)

Discrete Structures is a subject in computer science engineering which basically deals in Mathematics and it is commonly referred as Discrete mathematics 

Hence we can define it as ,Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

Now what does Discrete and Continuous means?
So, basically Discrete means distinct and Continuous means without interruption 

Continuous Structures − It is based upon continuous number line or the real numbers. It is characterized by the fact that between any two numbers, there are almost always an infinite set of numbers. For example, a function in continuous mathematics can be plotted in a smooth curve without breaks.

Discrete Mathematics − It involves distinct values; i.e. between any two points, there are a countable number of points. For example, if we have a finite set of objects, the function can be defined as a list of ordered pairs having these objects, and can be presented as a complete list of those pairs.


The Topics which we are going to study are as follows :-

• Sets, Relations and Functions
• Mathematical Logic
• Group theory
• Counting Theory
• Probability
• Mathematical Induction and Recurrence Relations
• Graph Theory
• Trees
• Boolean Algebra

I will be dealing with each and every topics in coming posts.