Discrete mathematics is a distinct mathematical term rather than being continuous term. Graph, integers, etc. are the part of discrete mathematics it excludes the topics such as of Calculus and analysis, etc. or in short we can say discrete mathematics deals with the countable Sets. As such there is no specified definition of discrete mathematics.
Graph in discrete mathematics can be studied with the help of graph theory which is also considered as the part of combinatorics, but in the present era it is a separate branch of mathematics first investigated by D.König in the year 1930.
Also graphs are considered to be the prime subject in the discrete mathematics. graph theory discrete mathematics is considered among the omnipresent model of both the natural and the structures which are made by man. They can mold many type structures and Relations such as method dynamics in physical, social and biological system. They have their several uses in many fields like in computer science they represent communication network, organization of data, help in the flow of computation, data organization, etc. in the field of mathematics, they can be used in the Geometry and also in many areas of topology. Also the group theory has a close link with the algebraic graph theory.
Discrete mathematics is also known as finite mathematics and the decision mathematics. As it is given above that it studies the countable Sets but it is different from continuous graph, we must not mix continuous graph with the graph theory. The graphs in discrete mathematics are of the many types few of them are simple graph, multi graph, directed graph, pseudo graph and many more. Now we will see brief description about these graphs:
1. The simple graphs are un- weighted and not in the particular direction and they have no loops but they have multiple edges.
2. The graphs which have multiple edges are multiple graphs.
3. The graphs which are connected with the Set of nodes and with its edges are directed graph.
4. Pseudo graph has the multiple edges and the graph loops connect them.
In field of science, graph theory is one of the very important concepts which describes that how a graph models different type of mathematical structures and also it can be used for all those structures which are created by human beings.
Also graphs are ubiquitous models which may be useful for various Relations.
Graphs has wide use due to their practical im...Read More
Path can be defined as distance traveled by an object from one Point to another. Points are called vertices of the path. Let there be two vertices A and B, then path between these two vertices is called A – B path. The distance between these two points or vertices is known as edge. Hence a path may include several vertices and edges. The Set of vertices and edges ac...Read More
Cycle graph can be defined as a graph which is comprised of single cycle. In other words, if vertices in given graph are connected in a closed form then graph is called as cycle graph. A cycle graph may can also be referred to circular graph. In a cycle graph, if there are 'n' vertices then cycle graph will be denoted by C n and number of vertices (nodes) in C n is...Read More
Connectivity is related to the network flow problems. It is used to find out the minimum number of vertices or edges which can be used to disconnect the remaining nodes from each other. Connectivity of a graph actually shows the robustness of the graph. If there are two nodes or vertices A and B, then they will be said connected if there is a path from A to ...Read More